Calculus Examples

${(x^{5})}^{2}$

Step 1

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{d}{d x} [x^{5 \cdot 2}]$

Step 1.2

Multiply $5$ by $2$ .

$\frac{d}{d x} [x^{10}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 10$ .

$10 x^{9}$