What is the derivative of 8sqrt(7x^2+5) ?

The derivative of 8sqrt(7x^2+5) is (56x)/(sqrt(7x^2+5))

What is the first derivative of 8sqrt(7x^2+5) ?

The first derivative of 8sqrt(7x^2+5) is (56x)/(sqrt(7x^2+5))

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\frac{d}{d x} (8 7 x^{2} + 5)

\frac{56 x}{7 x ^{2} + 5}

Solution steps

\frac{d}{d x} (8 7 x^{2} + 5)

Take the constant out:

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

= 8 \frac{d}{d x} (7 x^{2} + 5)

Apply the chain rule:

\frac{1}{2 7 x ^{2} + 5} \frac{d}{d x} (7 x^{2} + 5)

= \frac{1}{2 7 x ^{2} + 5} \frac{d}{d x} (7 x^{2} + 5)

\frac{d}{d x} (7 x^{2} + 5) = 14 x

= 8 \cdot \frac{1}{2 7 x ^{2} + 5} \cdot 14 x

Simplify

8 \cdot \frac{1}{2 7 x ^{2} + 5} \cdot 14 x : \frac{56 x}{7 x ^{2} + 5}

= \frac{56 x}{7 x ^{2} + 5}

What is the derivative of 8sqrt(7x^2+5) ?
The derivative of 8sqrt(7x^2+5) is (56x)/(sqrt(7x^2+5))
What is the first derivative of 8sqrt(7x^2+5) ?
The first derivative of 8sqrt(7x^2+5) is (56x)/(sqrt(7x^2+5))