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Popular >

derivative of 6sqrt(4x^2+5)

Solution

derivative of

6 4 x^{2} + 5

Solution

\frac{24 x}{4 x ^{2} + 5}

Solution steps

\frac{d}{d x} (6 4 x^{2} + 5)

Take the constant out:

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

= 6 \frac{d}{d x} (4 x^{2} + 5)

Apply the chain rule:

\frac{1}{2 4 x ^{2} + 5} \frac{d}{d x} (4 x^{2} + 5)

= \frac{1}{2 4 x ^{2} + 5} \frac{d}{d x} (4 x^{2} + 5)

\frac{d}{d x} (4 x^{2} + 5) = 8 x

= 6 \cdot \frac{1}{2 4 x ^{2} + 5} \cdot 8 x

Simplify

6 \cdot \frac{1}{2 4 x ^{2} + 5} \cdot 8 x : \frac{24 x}{4 x ^{2} + 5}

= \frac{24 x}{4 x ^{2} + 5}

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Frequently Asked Questions (FAQ)

What is the derivative of 6sqrt(4x^2+5) ?
The derivative of 6sqrt(4x^2+5) is (24x)/(sqrt(4x^2+5))
What is the first derivative of 6sqrt(4x^2+5) ?
The first derivative of 6sqrt(4x^2+5) is (24x)/(sqrt(4x^2+5))