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Popular >

derivative of 8sqrt(4x^2+7)

Solution

\frac{d}{d x} (8 4 x^{2} + 7)

Solution

\frac{32 x}{4 x ^{2} + 7}

Solution steps

\frac{d}{d x} (8 4 x^{2} + 7)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (4 x^{2} + 7)

Apply the chain rule:

\frac{1}{2 4 x ^{2} + 7} \frac{d}{d x} (4 x^{2} + 7)

= \frac{1}{2 4 x ^{2} + 7} \frac{d}{d x} (4 x^{2} + 7)

\frac{d}{d x} (4 x^{2} + 7) = 8 x

= 8 \cdot \frac{1}{2 4 x ^{2} + 7} \cdot 8 x

Simplify

8 \cdot \frac{1}{2 4 x ^{2} + 7} \cdot 8 x : \frac{32 x}{4 x ^{2} + 7}

= \frac{32 x}{4 x ^{2} + 7}

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Frequently Asked Questions (FAQ)

What is the derivative of 8sqrt(4x^2+7) ?
The derivative of 8sqrt(4x^2+7) is (32x)/(sqrt(4x^2+7))
What is the first derivative of 8sqrt(4x^2+7) ?
The first derivative of 8sqrt(4x^2+7) is (32x)/(sqrt(4x^2+7))