Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67301	Find dy/dx	y=(csc(x)-cot(x))^-1	$y = {(\csc (x) - \cot (x))}^{- 1}$
67302	Evaluate the Integral	integral of (x^(3/2)-2x^(2/3)+5 square root of x-3) with respect to x	$\int (x^{\frac{3}{2}} - 2 x^{\frac{2}{3}} + 5 \sqrt{x} - 3) d x$
67303	Solve the Differential Equation	(dy)/(dx)+2xy^2=0	$\frac{d y}{d x} + 2 x y^{2} = 0$
67304	Find the Derivative - d/dθ	y=sec(theta)(theta-tan(theta))	$y = \sec (θ) (θ - \tan (θ))$
67305	Use Logarithmic Differentiation to Find the Derivative	y=x^(sin(x))	$y = x^{\sin (x)}$
67306	Evaluate the Integral	integral of 3sec(2t)^2 with respect to t	$\int 3 \sec^{2} (2 t) d t$
67307	Find dy/dx	e^y-e^(y^2)=x-x^3	$e^{y} - e^{y^{2}} = x - x^{3}$
67308	Find dy/dx	y=sin(x)cos(x)	$y = \sin (x) \cos (x)$
67309	Determine if Continuous	f(x)=x^2+1 if x<1; 2 if x=1; 8-3x if x>1	$f (x) = {\begin{cases} x^{2} + 1 & x < 1 \\ 2 & x = 1 \\ 8 - 3 x & x > 1 \end{cases}$
67310	Find dy/dx	(x^2)/(x+y)=y^2+3	$\frac{x^{2}}{x + y} = y^{2} + 3$
67311	Determine if Continuous	f(x)=-5x+3 if x<=2; x-4 if x>2	$f (x) = {\begin{cases} - 5 x + 3 & x \leq 2 \\ x - 4 & x > 2 \end{cases}$
67312	Find the Slope	-1	$- 1$
67313	Find the Derivative - d/dx	d/(dx)(sin(x)^2)	$\frac{d}{d x} (\sin^{2} (x))$
67314	Find the Maximum/Minimum Value	f(x)=ax^2+bx+c	$f (x) = a x^{2} + b x + c$
67315	Find dV/dr	V=pir^2h	$V = π r^{2} h$
67316	Find the Center and Radius	x^2+y^2+3x+y+10=0	$x^{2} + y^{2} + 3 x + y + 10 = 0$
67317	Determine if Continuous	f(x)=-x^2+10 if -4<=x<4; -5-x if x>=4	$f (x) = {\begin{cases} - x^{2} + 10 & - 4 \leq x < 4 \\ - 5 - x & x \geq 4 \end{cases}$
67318	Find the Derivative - d/dx	1/(x^3)-1/x+x^2	$\frac{1}{x^{3}} - \frac{1}{x} + x^{2}$
67319	Find the Derivative - d/dx	d/(dx)(3e^x+5x^2)	$\frac{d}{d x} (3 e^{x} + 5 x^{2})$
67320	Determine if Continuous	f(x)=4x+3 if x<=-2; x-2 if x>-2	$f (x) = {\begin{cases} 4 x + 3 & x \leq - 2 \\ x - 2 & x > - 2 \end{cases}$
67321	Find the Maximum/Minimum Value	P(x)=-2(x-9)^2+200	$P (x) = - 2 {(x - 9)}^{2} + 200$
67322	Find Where Increasing/Decreasing	f(x)=(x^2)/(x^2-4)	$f (x) = \frac{x^{2}}{x^{2} - 4}$
67323	Find dy/dx	xcos(y)=1	$x \cos (y) = 1$
67324	Find the Derivative - d/dx	square root of 4	$\sqrt{4}$
67325	Find dy/dx	x^2y^2=9	$x^{2} y^{2} = 9$
67326	Find dy/dx	x^3+y^3=6xy-1	$x^{3} + y^{3} = 6 x y - 1$
67327	Find dy/dx	x^2y^2=x^2+y^2	$x^{2} y^{2} = x^{2} + y^{2}$
67328	Evaluate the Limit	limit as x approaches infinity of (x+4)/(x-4)	$lim_{x \to \infty} \frac{x + 4}{x - 4}$
67329	Evaluate the Integral	integral from 0 to pi/2 of 7cos(theta)^2 with respect to theta	$\int_{0}^{\frac{π}{2}} 7 \cos^{2} (θ) d θ$
67330	Find dy/dx	y=cos(x)^2	$y = \cos^{2} (x)$
67331	Find the Slope	-3/4	$- \frac{3}{4}$
67332	Find the Integral	xsin(x)	$x \sin (x)$
67333	Integrate By Parts	integral of xe^(5x) with respect to x	$\int x e^{5 x} d x$
67334	Evaluate the Summation	sum from 0 to 10 of x^2	$\sum_{0}^{10} x^{2}$
67335	Evaluate the Limit	limit as x approaches 2 of (x-2)/(x^2+x-6)	$lim_{x \to 2} \frac{x - 2}{x^{2} + x - 6}$
67336	Evaluate the Limit	limit as x approaches infinity of (-5x^4+2x)/(x^3)	$lim_{x \to \infty} \frac{- 5 x^{4} + 2 x}{x^{3}}$
67337	Find dy/dx	y=(cot(x)+csc(x))^-1	$y = {(\cot (x) + \csc (x))}^{- 1}$
67338	Find dy/dx	3x-tan(y)=4	$3 x - \tan (y) = 4$
67339	Evaluate the Limit	limit as x approaches negative infinity of x/( square root of x^2+1)	$lim_{x \to - \infty} \frac{x}{\sqrt{x^{2} + 1}}$
67340	Determine if Continuous	f(x)=5x-4 if x<=1; -x+4 if x>1	$f (x) = {\begin{cases} 5 x - 4 & x \leq 1 \\ - x + 4 & x > 1 \end{cases}$
67341	Evaluate the Limit	limit as x approaches a of ( square root of x- square root of a)/(x-a)	$lim_{x \to a} \frac{\sqrt{x} - \sqrt{a}}{x - a}$
67342	Evaluate the Integral	integral of (3/(x^5)-2/(x^2)-6/x) with respect to x	$\int (\frac{3}{x^{5}} - \frac{2}{x^{2}} - \frac{6}{x}) d x$
67343	Find the Tangent at a Given Point Using the Limit Definition	7x^2+3x , (1,10)	$7 x^{2} + 3 x$ , $(1, 10)$
67344	Find the Derivative - d/da	ax	$a x$
67345	Evaluate the Limit	limit as x approaches 0 of x/(3- square root of x+9)	$lim_{x \to 0} \frac{x}{3 - \sqrt{x + 9}}$
67346	Find dy/dx	y square root of x+1=4	$y \sqrt{x + 1} = 4$
67347	Evaluate the Integral	integral of ( square root of 4)/x with respect to x	$\int \frac{\sqrt{4}}{x} d x$
67348	Evaluate the Integral	integral from 0 to 2 of 1/(x^2-2x+2) with respect to x	$\int_{0}^{2} \frac{1}{x^{2} - 2 x + 2} d x$
67349	Find the Maximum/Minimum Value	y=-4x^2	$y = - 4 x^{2}$
67350	Find dy/dx	square root of xy=x-2y	$\sqrt{x y} = x - 2 y$
67351	Find the Derivative - d/dx	x^2e^x+2xe^x	$x^{2} e^{x} + 2 x e^{x}$
67352	Find dy/dx	x=csc(y)	$x = \csc (y)$
67353	Find dy/dx	y^2=x^3	$y^{2} = x^{3}$
67354	Integrate Using Trig Substitution	integral of ( square root of 9-x^2)/(x^2) with respect to x	$\int \frac{\sqrt{9 - x^{2}}}{x^{2}} d x$
67355	Find dy/dx	y = square root of f(x)	$y = \sqrt{f (x)}$
67356	Evaluate the Limit	limit as x approaches 3 of ( square root of x+6-x)/(x^3-3x^2)	$lim_{x \to 3} \frac{\sqrt{x + 6} - x}{x^{3} - 3 x^{2}}$
67357	Find the Derivative - d/dx	(sin(x))/(e^x)	$\frac{\sin (x)}{e^{x}}$
67358	Evaluate the Integral	integral of (2x-3x^2) with respect to x	$\int (2 x - 3 x^{2}) d x$
67359	Find the Derivative - d/dx	2pix	$2 π x$
67360	Find dy/dx	4x-x^2y+y^3=10	$4 x - x^{2} y + y^{3} = 10$
67361	Evaluate the Limit	limit as x approaches -5 of 2^x-x	$lim_{x \to - 5} 2^{x} - x$
67362	Find the Derivative - d/dx	d/(dx)e^(-x)	$\frac{d}{d x} e^{- x}$
67363	Find the Derivative - d/dx	(sin(x)+cos(x))/(e^x)	$\frac{\sin (x) + \cos (x)}{e^{x}}$
67364	Evaluate the Integral	integral of (3/4x^4+3x^2+1) with respect to x	$\int (\frac{3}{4} x^{4} + 3 x^{2} + 1) d x$
67365	Find dy/dx	y=1/(x^3)	$y = \frac{1}{x^{3}}$
67366	Find dx/dy	x^2-4xy+y^2=4	$x^{2} - 4 x y + y^{2} = 4$
67367	Evaluate the Integral	integral of (2/( square root of x)+2 square root of x) with respect to x	$\int (\frac{2}{\sqrt{x}} + 2 \sqrt{x}) d x$
67368	Find dy/dx	x^2+y^2=2xy	$x^{2} + y^{2} = 2 x y$
67369	Find the Integral	-1/x	$- \frac{1}{x}$
67370	Find Where Increasing/Decreasing	f(x)=x/(x^2+9)	$f (x) = \frac{x}{x^{2} + 9}$
67371	Evaluate the Limit	limit as x approaches infinity of (5x^4+x^2)/(2x^4-x^3-4)	$lim_{x \to \infty} \frac{5 x^{4} + x^{2}}{2 x^{4} - x^{3} - 4}$
67372	Evaluate the Limit	limit as x approaches infinity of (3x-1)/( square root of x^2-6)	$lim_{x \to \infty} \frac{3 x - 1}{\sqrt{x^{2} - 6}}$
67373	Find dy/dx	y = square root of 4x+2	$y = \sqrt{4 x + 2}$
67374	Determine if Continuous	f(x)=8 if x<-4; -10+x^2 if -4<=x<4; 2x-2 if x>=4	$f (x) = {\begin{cases} 8 & x < - 4 \\ - 10 + x^{2} & - 4 \leq x < 4 \\ 2 x - 2 & x \geq 4 \end{cases}$
67375	Find dy/dx	2x^2+y^2=4	$2 x^{2} + y^{2} = 4$
67376	Find dy/dx	y=2 square root of x	$y = 2 \sqrt{x}$
67377	Find the Derivative - d/dx	d/(dx)(7cos(x)+3e^x)	$\frac{d}{d x} (7 \cos (x) + 3 e^{x})$
67378	Find dy/dx	x^2-y^2=25	$x^{2} - y^{2} = 25$
67379	Find the Antiderivative	1/(x^2-1)	$\frac{1}{x^{2} - 1}$
67380	Find the Derivative - d/dx	f(x)*g(x)	$f (x) \cdot g (x)$
67381	Find the Root Mean Square	y=x-2 , (2,7)	$y = x - 2$ , $(2, 7)$
67382	Determine if Continuous	f(x)=x-3 if x<=-2; 4x+5 if x>-2	$f (x) = {\begin{cases} x - 3 & x \leq - 2 \\ 4 x + 5 & x > - 2 \end{cases}$
67383	Find the Tangent Line at (-3√(3),1)	x^(2/3)+y^(2/3)=4 , (-3 square root of 3,1)	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ , $(- 3 \sqrt{3}, 1)$
67384	Determine if Continuous	f(x)=x^2+1 if x<1; 2 if x=1; 7-5x if x>1	$f (x) = {\begin{cases} x^{2} + 1 & x < 1 \\ 2 & x = 1 \\ 7 - 5 x & x > 1 \end{cases}$
67385	Find the Maximum/Minimum Value	y=(x-2)^2+3	$y = {(x - 2)}^{2} + 3$
67386	Evaluate the Integral	integral from 0 to 2 of (4x+1)^3*4 with respect to x	$\int_{0}^{2} {(4 x + 1)}^{3} \cdot 4 d x$
67387	Find the Derivative - d/dx	(x/(x+1))^5	${(\frac{x}{x + 1})}^{5}$
67388	Evaluate the Integral	integral of (x^-3+x^-2+x^-1) with respect to x	$\int (x^{- 3} + x^{- 2} + x^{- 1}) d x$
67389	Find dy/dx	y=x^-3	$y = x^{- 3}$
67390	Find dy/dx	sin(x+y)=3x-2y	$\sin (x + y) = 3 x - 2 y$
67391	Find dz/dx	z=e^(xy)	$z = e^{x y}$
67392	Evaluate the Integral	integral of (2e^x+4^x) with respect to x	$\int (2 e^{x} + 4^{x}) d x$
67393	Find dx/dy	x^3+y^3=1	$x^{3} + y^{3} = 1$
67394	Find the Derivative - d/dx	d/(dx)csc(x)	$\frac{d}{d x} \csc (x)$
67395	Find the Derivative - d/dx	y=3/4x	$y = \frac{3}{4} x$
67396	Evaluate the Limit	limit as x approaches infinity of (x+1)/(x^2+1)	$lim_{x \to \infty} \frac{x + 1}{x^{2} + 1}$
67397	Integrate Using u-Substitution	integral of x square root of x+1 with respect to x	$\int x \sqrt{x + 1} d x$
67398	Find dy/dx	ysin(x^2)=xsin(y^2)	$y \sin (x^{2}) = x \sin (y^{2})$
67399	Find the Maximum/Minimum Value	f(x)=-x^4-x^3+3x^2+2x	$f (x) = - x^{4} - x^{3} + 3 x^{2} + 2 x$
67400	Find the Tangent Line at (3π,0)	y=sin(sin(x)) , (3pi,0)	$y = \sin (\sin (x))$ , $(3 π, 0)$