Calculus Examples

$g (u) = 2 u^{h} (5 h^{2} + 3 h)$

Step 1

Since $2 (5 h^{2} + 3 h)$ is constant with respect to $u$ , the derivative of $2 u^{h} (5 h^{2} + 3 h)$ with respect to $u$ is $2 (5 h^{2} + 3 h) \frac{d}{d u} [u^{h}]$ .

$2 (5 h^{2} + 3 h) \frac{d}{d u} [u^{h}]$

Step 2

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

$2 (5 h^{2} + 3 h) (h u^{h - 1})$

Step 3

Simplify.

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Step 3.1

Apply the distributive property.

$(2 (5 h^{2}) + 2 (3 h)) (h u^{h - 1})$

Step 3.2

Combine terms.

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Step 3.2.1

Multiply $5$ by $2$ .

$(10 h^{2} + 2 (3 h)) (h u^{h - 1})$

Step 3.2.2

Multiply $3$ by $2$ .

$(10 h^{2} + 6 h) h u^{h - 1}$

Step 3.3

Reorder the factors of $(10 h^{2} + 6 h) h u^{h - 1}$ .

$u^{h - 1} h (10 h^{2} + 6 h)$