Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67201	Find dy/dx	3x^2-x^2y+y^4=1	$3 x^{2} - x^{2} y + y^{4} = 1$
67202	Find dy/dx	x^(2/3)+y^(2/3)=5	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5$
67203	Find dy/dx	y=(sin(x))/(1+sin(x))	$y = \frac{\sin (x)}{1 + \sin (x)}$
67204	Evaluate the Integral	integral of (x-19)/(x^2-3x-10) with respect to x	$\int \frac{x - 19}{x^{2} - 3 x - 10} d x$
67205	Find dy/dx	2x^3+x^2y-xy^3=2	$2 x^{3} + x^{2} y - x y^{3} = 2$
67206	Find dy/dx	y=(cos(x))/(1+cos(x))	$y = \frac{\cos (x)}{1 + \cos (x)}$
67207	Evaluate the Integral	integral of (x^3+2x^2) with respect to x	$\int (x^{3} + 2 x^{2}) d x$
67208	Find dy/dx	y=sin(x)	$y = \sin (x)$
67209	Find dy/dx	xy+x+y=x^2y^2	$x y + x + y = x^{2} y^{2}$
67210	Evaluate the Limit	limit as x approaches negative infinity of (5x^3-3x)/( square root of 4x^6-7)	$lim_{x \to - \infty} \frac{5 x^{3} - 3 x}{\sqrt{4 x^{6} - 7}}$
67211	Find the Maximum/Minimum Value	f(x)=x^3-4x	$f (x) = x^{3} - 4 x$
67212	Find the Antiderivative	f(x)	$f (x)$
67213	Find dx/dy	2xy-y^2=1	$2 x y - y^{2} = 1$
67214	Find dy/dx	y=29^x	$y = 29^{x}$
67215	Find dy/dx	y = cube root of 1+5x	$y = \sqrt[3]{1 + 5 x}$
67216	Find the Antiderivative	f(x)=x^(-5/2)+2x^-3+2x+4	$f (x) = x^{- \frac{5}{2}} + 2 x^{- 3} + 2 x + 4$
67217	Find dy/dx	x^4+y^4=16	$x^{4} + y^{4} = 16$
67218	Evaluate the Integral	integral from 2 to 6 of 1/((x^2-1)^(3/2)) with respect to x	$\int_{2}^{6} \frac{1}{{(x^{2} - 1)}^{\frac{3}{2}}} d x$
67219	Find dy/dx	y=(cot(x)-csc(x))^-1	$y = {(\cot (x) - \csc (x))}^{- 1}$
67220	Evaluate the Integral	integral of 2xy with respect to x	$\int 2 x y d x$
67221	Find dy/dx	x^2+xy+y^2=7	$x^{2} + x y + y^{2} = 7$
67222	Find dy/dx	y=x^4e^x	$y = x^{4} e^{x}$
67223	Integrate By Parts	integral of x^2sin(x) with respect to x	$\int x^{2} \sin (x) d x$
67224	Find the Derivative - d/dx	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
67225	Evaluate the Integral	integral of (2x)^3 with respect to x	$\int {(2 x)}^{3} d x$
67226	Evaluate the Limit	limit as x approaches infinity of (2x^4-7)/( square root of 4x^8+7x^5)	$lim_{x \to \infty} \frac{2 x^{4} - 7}{\sqrt{4 x^{8} + 7 x^{5}}}$
67227	Find dy/dx	x^2y-3x^2-4=0	$x^{2} y - 3 x^{2} - 4 = 0$
67228	Determine if Continuous	f(x)=1-x^2 if x<1; -2x+2 if x>=1	$f (x) = {\begin{cases} 1 - x^{2} & x < 1 \\ - 2 x + 2 & x \geq 1 \end{cases}$
67229	Find the Derivative - d/dθ	tan(theta)^2	$\tan^{2} (θ)$
67230	Evaluate the Integral	integral of (4/( square root of x)- cube root of x^2) with respect to x	$\int (\frac{4}{\sqrt{x}} - \sqrt[3]{x^{2}}) d x$
67231	Evaluate the Integral	integral of ( square root of x^3-5/( square root of x)) with respect to x	$\int (\sqrt{x^{3}} - \frac{5}{\sqrt{x}}) d x$
67232	Evaluate the Integral	integral from 0 to 2 of (x^2-2x) with respect to x	$\int_{0}^{2} (x^{2} - 2 x) d x$
67233	Determine if Continuous	f(x)=-x+2 if x<=1; 5x-2 if x>1	$f (x) = {\begin{cases} - x + 2 & x \leq 1 \\ 5 x - 2 & x > 1 \end{cases}$
67234	Find the Integral	cot(x)^2	$\cot^{2} (x)$
67235	Find the Center and Radius	((x+5)^2)/5+((y+9)^2)/9	$\frac{{(x + 5)}^{2}}{5} + \frac{{(y + 9)}^{2}}{9}$
67236	Find dy/dx	e^(x/y)=8x-y	$e^{\frac{x}{y}} = 8 x - y$
67237	Find the Maximum/Minimum Value	y=x^3	$y = x^{3}$
67238	Find the Antiderivative	f''''(x)=5x^4	$f'' (x) = 5 x^{4}$
67239	Find dx/dy	y=e^x	$y = e^{x}$
67240	Find dy/dx	arcsin(x) = natural log of y	$\arcsin (x) = \ln (y)$
67241	Find dy/dx	x=y^2	$x = y^{2}$
67242	Use Logarithmic Differentiation to Find the Derivative	y=x^(4x)	$y = x^{4 x}$
67243	Evaluate the Limit	limit as theta approaches pi/4 of (cos(2theta))/( square root of 2cos(theta)-1)	$lim_{θ \to \frac{π}{4}} \frac{\cos (2 θ)}{\sqrt{2} \cos (θ) - 1}$
67244	Integrate By Parts	integral of square root of x natural log of x with respect to x	$\int \sqrt{x} \ln (x) d x$
67245	Find dy/dx	4cos(x)sin(y)=1	$4 \cos (x) \sin (y) = 1$
67246	Find dy/dx	e^(x/y)=3x-y	$e^{\frac{x}{y}} = 3 x - y$
67247	Find the Tangent Line at (1,e)	y=(e^x)/x , (1,e)	$y = \frac{e^{x}}{x}$ , $(1, e)$
67248	Find dy/dx	y=cos(x)	$y = \cos (x)$
67249	Evaluate the Limit	limit as x approaches infinity of (5x^2+4)/( square root of 4x^4+5x)	$lim_{x \to \infty} \frac{5 x^{2} + 4}{\sqrt{4 x^{4} + 5 x}}$
67250	Evaluate the Integral	integral from 2 to 3 of 1/((x^2-1)^(3/2)) with respect to x	$\int_{2}^{3} \frac{1}{{(x^{2} - 1)}^{\frac{3}{2}}} d x$
67251	Find the Antiderivative	t	$t$
67252	Find dy/dx	square root of x+ square root of y=4	$\sqrt{x} + \sqrt{y} = 4$
67253	Evaluate the Limit	limit as x approaches 0 of (sin(x)-sin(x)cos(x))/(x^2)	$lim_{x \to 0} \frac{\sin (x) - \sin (x) \cos (x)}{x^{2}}$
67254	Find the Derivative - d/dx	y=(4x^2-16)/(x-2)	$y = \frac{4 x^{2} - 16}{x - 2}$
67255	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of x^x	$lim_{x \to 0^{+}} x^{x}$
67256	Evaluate the Integral	integral from 3 to infinity of 1/((x-2)^(3/2)) with respect to x	$\int_{3}^{\infty} \frac{1}{{(x - 2)}^{\frac{3}{2}}} d x$
67257	Find dy/dx	square root of 2x+2y=6x	$\sqrt{2 x + 2 y} = 6 x$
67258	Find dy/dx	tan(y)=x	$\tan (y) = x$
67259	Find dy/dx	y=xy+x^2+1	$y = x y + x^{2} + 1$
67260	Find the Second Derivative	f(x)=x square root of x^2+1	$f (x) = x \sqrt{x^{2}} + 1$
67261	Find Where Increasing/Decreasing	f(x)=e^(-x^2)	$f (x) = e^{- x^{2}}$
67262	Evaluate the Summation	Find sum from k=4 to 18 of 6k-1	Find $\sum_{k = 4}^{18} 6 k - 1$
67263	Find the Maximum/Minimum Value	y=2x^3+3x^2-12x	$y = 2 x^{3} + 3 x^{2} - 12 x$
67264	Determine if Continuous	f(x)=-x^2+10 if -4<=x<4; 6-3x if x>=4	$f (x) = {\begin{cases} - x^{2} + 10 & - 4 \leq x < 4 \\ 6 - 3 x & x \geq 4 \end{cases}$
67265	Evaluate the Integral	integral of sec(x)(sec(x)-tan(x)) with respect to x	$\int \sec (x) (\sec (x) - \tan (x)) d x$
67266	Find the Tangent Line at (4π,0)	y=sin(sin(x)) , (4pi,0)	$y = \sin (\sin (x))$ , $(4 π, 0)$
67267	Find dy/dx	x^3-xy+y^2=4	$x^{3} - x y + y^{2} = 4$
67268	Evaluate the Integral	integral from -pi to pi of (pi^2+2x) with respect to x	$\int_{- π}^{π} (π^{2} + 2 x) d x$
67269	Find dy/dx	x^3y+y^2-x^2=5	$x^{3} y + y^{2} - x^{2} = 5$
67270	Find dy/dx	3x^2+y^2=9	$3 x^{2} + y^{2} = 9$
67271	Find dy/dx	y = natural log of x^2+y^2	$y = \ln (x^{2} + y^{2})$
67272	Find dy/dx	y=e^(3x)	$y = e^{3 x}$
67273	Find the Antiderivative	f(x)=(x^2+x)^10(2x+1)	$f (x) = {(x^{2} + x)}^{10} (2 x + 1)$
67274	Find dy/dx	2x^3+x^2y+y^2=4	$2 x^{3} + x^{2} y + y^{2} = 4$
67275	Find dy/dx	tan(x+y)=x	$\tan (x + y) = x$
67276	Find dy/dx	y^2=(x-1)/(x+1)	$y^{2} = \frac{x - 1}{x + 1}$
67277	Find dy/dx	xy^2=4	$x y^{2} = 4$
67278	Evaluate the Integral	integral of (x^3+3x^2) with respect to x	$\int (x^{3} + 3 x^{2}) d x$
67279	Evaluate the Limit	limit as x approaches -5 of (10x^2+50x)/(x^2-25)	$lim_{x \to - 5} \frac{10 x^{2} + 50 x}{x^{2} - 25}$
67280	Find the Integral	square root of xdx	$\sqrt{x} d x$
67281	Find dy/dx	y^4+3xy+x=2	$y^{4} + 3 x y + x = 2$
67282	Find the Antiderivative	f(x)=(x+1)^100	$f (x) = {(x + 1)}^{100}$
67283	Evaluate the Integral	integral from -pi/3 to pi/3 of [(-sec(x))-(-2)] with respect to x	$\int_{- \frac{π}{3}}^{\frac{π}{3}} [(- \sec (x)) - (- 2)] d x$
67284	Evaluate the Integral	integral of (e^(3x)+5) with respect to x	$\int (e^{3 x} + 5) d x$
67285	Evaluate the Limit	limit as x approaches infinity of (10-6x^2)/(5+3e^x)	$lim_{x \to \infty} \frac{10 - 6 x^{2}}{5 + 3 e^{x}}$
67286	Evaluate the Limit	limit as x approaches infinity of (4x^3)/(x^2+20x)	$lim_{x \to \infty} \frac{4 x^{3}}{x^{2} + 20 x}$
67287	Evaluate the Integral	integral from 1 to 2 of (1/(x^2)-4/(x^3)) with respect to x	$\int_{1}^{2} (\frac{1}{x^{2}} - \frac{4}{x^{3}}) d x$
67288	Evaluate the Limit	limit as x approaches negative infinity of (3x)/( square root of 16x^2-9x)	$lim_{x \to - \infty} \frac{3 x}{\sqrt{16 x^{2} - 9 x}}$
67289	Find the Derivative - d/dx	(sin(x)+cos(x))	$(\sin (x) + \cos (x))$
67290	Find dy/dx	y=x^7e^x	$y = x^{7} e^{x}$
67291	Find the Maximum/Minimum Value	y=x^3-3x^2	$y = x^{3} - 3 x^{2}$
67292	Find the Derivative - d/dx	y=(sin(x)+cos(x))/(e^x)	$y = \frac{\sin (x) + \cos (x)}{e^{x}}$
67293	Find dy/dx	y=(x/(x+1))^5	$y = {(\frac{x}{x + 1})}^{5}$
67294	Find dy/dx	y=3x	$y = 3 x$
67295	Find dy/dx	x^2-y^2=1	$x^{2} - y^{2} = 1$
67296	Find dy/dx	y=(x^3+1)^2	$y = {(x^{3} + 1)}^{2}$
67297	Evaluate the Integral	integral from 0 to infinity of xe^(-x^2) with respect to x	$\int_{0}^{\infty} x e^{- x^{2}} d x$
67298	Determine if Continuous	f(x)=1-x^2 if x<1; -2x-3 if x>=1	$f (x) = {\begin{cases} 1 - x^{2} & x < 1 \\ - 2 x - 3 & x \geq 1 \end{cases}$
67299	Evaluate the Integral	integral from -2 to 2 of (4-x^2) with respect to x	$\int_{- 2}^{2} (4 - x^{2}) d x$
67300	Evaluate the Integral	integral from 0 to pi/2 of 3cos(theta)^2 with respect to theta	$\int_{0}^{\frac{π}{2}} 3 \cos^{2} (θ) d θ$