What is the derivative of sqrt(8x^2+7) ?

The derivative of sqrt(8x^2+7) is (8x)/(sqrt(8x^2+7))

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

The first derivative of sqrt(8x^2+7) is (8x)/(sqrt(8x^2+7))

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

\frac{8 x}{8 x ^{2} + 7}

Solution steps

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

Apply the chain rule:

\frac{1}{2 8 x ^{2} + 7} \frac{d}{d x} (8 x^{2} + 7)

= \frac{1}{2 8 x ^{2} + 7} \frac{d}{d x} (8 x^{2} + 7)

\frac{d}{d x} (8 x^{2} + 7) = 16 x

= \frac{1}{2 8 x ^{2} + 7} \cdot 16 x

Simplify

\frac{1}{2 8 x ^{2} + 7} \cdot 16 x : \frac{8 x}{8 x ^{2} + 7}

= \frac{8 x}{8 x ^{2} + 7}

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