What is the derivative of 8sqrt(7x^2+3) ?

The derivative of 8sqrt(7x^2+3) is (56x)/(sqrt(7x^2+3))

What is the first derivative of 8sqrt(7x^2+3) ?

The first derivative of 8sqrt(7x^2+3) is (56x)/(sqrt(7x^2+3))

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derivative of

8 7 x^{2} + 3

\frac{56 x}{7 x ^{2} + 3}

Solution steps

\frac{d}{d x} (8 7 x^{2} + 3)

Take the constant out:

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

= 8 \frac{d}{d x} (7 x^{2} + 3)

Apply the chain rule:

\frac{1}{2 7 x ^{2} + 3} \frac{d}{d x} (7 x^{2} + 3)

= \frac{1}{2 7 x ^{2} + 3} \frac{d}{d x} (7 x^{2} + 3)

\frac{d}{d x} (7 x^{2} + 3) = 14 x

= 8 \cdot \frac{1}{2 7 x ^{2} + 3} \cdot 14 x

Simplify

8 \cdot \frac{1}{2 7 x ^{2} + 3} \cdot 14 x : \frac{56 x}{7 x ^{2} + 3}

= \frac{56 x}{7 x ^{2} + 3}

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What is the derivative of 8sqrt(7x^2+3) ?
The derivative of 8sqrt(7x^2+3) is (56x)/(sqrt(7x^2+3))
What is the first derivative of 8sqrt(7x^2+3) ?
The first derivative of 8sqrt(7x^2+3) is (56x)/(sqrt(7x^2+3))