Calculus Examples

$y = (2 x) (3 x^{3})$

Step 1

Multiply $3$ by $2$ .

$\frac{d}{d x} [6 x \cdot x^{3}]$

Step 2

Multiply $x$ by $x^{3}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $x^{3}$ .

$\frac{d}{d x} [6 (x^{3} x)]$

Step 2.2

Multiply $x^{3}$ by $x$ .

Tap for more steps...

Step 2.2.1

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [6 (x^{3} x^{1})]$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{d}{d x} [6 x^{3 + 1}]$

Step 2.3

Add $3$ and $1$ .

$\frac{d}{d x} [6 x^{4}]$

Step 3

Since $6$ is constant with respect to $x$ , the derivative of $6 x^{4}$ with respect to $x$ is $6 \frac{d}{d x} [x^{4}]$ .

$6 \frac{d}{d x} [x^{4}]$

Step 4

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 4$ .

$6 (4 x^{3})$

Step 5

Multiply $4$ by $6$ .

$24 x^{3}$