Calculus Examples

$3 x^{2} y$

Step 1

Find the first derivative.

Tap for more steps...

Step 1.1

Since $3 y$ is constant with respect to $x$ , the derivative of $3 x^{2} y$ with respect to $x$ is $3 y \frac{d}{d x} [x^{2}]$ .

$3 y \frac{d}{d x} [x^{2}]$

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$3 y (2 x)$

Step 1.3

Simplify the expression.

Tap for more steps...

Step 1.3.1

Multiply $2$ by $3$ .

$6 y x$

Step 1.3.2

Reorder the factors of $6 y x$ .

$f' (x) = 6 x y$

Step 2

Find the second derivative.

Tap for more steps...

Step 2.1

Since $6 y$ is constant with respect to $x$ , the derivative of $6 x y$ with respect to $x$ is $6 y \frac{d}{d x} [x]$ .

$6 y \frac{d}{d x} [x]$

Step 2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$6 y \cdot 1$

Step 2.3

Multiply $6$ by $1$ .

$f'' (x) = 6 y$