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Popular >

derivative of sqrt(2x^3+5x)

Solution

\frac{d}{d x} (2 x^{3} + 5 x)

Solution

\frac{6 x ^{2} + 5}{2 2 x ^{3} + 5 x}

Solution steps

\frac{d}{d x} (2 x^{3} + 5 x)

Apply the chain rule:

\frac{1}{2 2 x ^{3} + 5 x} \frac{d}{d x} (2 x^{3} + 5 x)

= \frac{1}{2 2 x ^{3} + 5 x} \frac{d}{d x} (2 x^{3} + 5 x)

\frac{d}{d x} (2 x^{3} + 5 x) = 6 x^{2} + 5

= \frac{1}{2 2 x ^{3} + 5 x} (6 x^{2} + 5)

Simplify

\frac{1}{2 2 x ^{3} + 5 x} (6 x^{2} + 5) : \frac{6 x ^{2} + 5}{2 2 x ^{3} + 5 x}

= \frac{6 x ^{2} + 5}{2 2 x ^{3} + 5 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2x^3+5x) ?
The derivative of sqrt(2x^3+5x) is (6x^2+5)/(2sqrt(2x^3+5x))
What is the first derivative of sqrt(2x^3+5x) ?
The first derivative of sqrt(2x^3+5x) is (6x^2+5)/(2sqrt(2x^3+5x))