What is the derivative of f(x)=6sqrt(5x^2+7) ?

The derivative of f(x)=6sqrt(5x^2+7) is (30x)/(sqrt(5x^2+7))

What is the first derivative of f(x)=6sqrt(5x^2+7) ?

The first derivative of f(x)=6sqrt(5x^2+7) is (30x)/(sqrt(5x^2+7))

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derivative of

f (x) = 6 5 x^{2} + 7

\frac{30 x}{5 x ^{2} + 7}

Solution steps

\frac{d}{d x} (6 5 x^{2} + 7)

Take the constant out:

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

= 6 \frac{d}{d x} (5 x^{2} + 7)

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{2} + 7) = 10 x

= 6 \cdot \frac{1}{2 5 x ^{2} + 7} \cdot 10 x

Simplify

6 \cdot \frac{1}{2 5 x ^{2} + 7} \cdot 10 x : \frac{30 x}{5 x ^{2} + 7}

= \frac{30 x}{5 x ^{2} + 7}

What is the derivative of f(x)=6sqrt(5x^2+7) ?
The derivative of f(x)=6sqrt(5x^2+7) is (30x)/(sqrt(5x^2+7))
What is the first derivative of f(x)=6sqrt(5x^2+7) ?
The first derivative of f(x)=6sqrt(5x^2+7) is (30x)/(sqrt(5x^2+7))