Calculus Examples

$y = 5 x^{4} (7 x^{5})$

Step 1

Multiply $7$ by $5$ .

$\frac{d}{d x} [35 x^{4} x^{5}]$

Step 2

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

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Step 2.1

Move $x^{5}$ .

$\frac{d}{d x} [35 (x^{5} x^{4})]$

Step 2.2

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

$\frac{d}{d x} [35 x^{5 + 4}]$

Step 2.3

Add $5$ and $4$ .

$\frac{d}{d x} [35 x^{9}]$

Step 3

Since $35$ is constant with respect to $x$ , the derivative of $35 x^{9}$ with respect to $x$ is $35 \frac{d}{d x} [x^{9}]$ .

$35 \frac{d}{d x} [x^{9}]$

Step 4

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 9$ .

$35 (9 x^{8})$

Step 5

Multiply $9$ by $35$ .

$315 x^{8}$