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Popular >

derivative of f(x)=sqrt(12x+\sqrt{x)}

Solution

derivative of

f (x) = 12 x + x

Solution

\frac{24 x + 1}{4 x 12 x + x}

Solution steps

\frac{d}{d x} (12 x + x)

Apply the chain rule:

\frac{1}{2 12 x + x} \frac{d}{d x} (12 x + x)

= \frac{1}{2 12 x + x} \frac{d}{d x} (12 x + x)

\frac{d}{d x} (12 x + x) = 12 + \frac{1}{2 x}

= \frac{1}{2 12 x + x} (12 + \frac{1}{2 x})

Simplify

\frac{1}{2 12 x + x} (12 + \frac{1}{2 x}) : \frac{24 x + 1}{4 x 12 x + x}

= \frac{24 x + 1}{4 x 12 x + x}

Popular Examples

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\frac{d}{d x} (sin^{2} (2 x) cos^{3} (3 x))

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x \to \infty lim ((4^{x} + 4^{x})^{\frac{1}{2 x}})

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\int \frac{x + 16}{x ^{2} + 2 x - 8} d x

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x \to 0 lim (x^{6} cos (\frac{4}{x}))

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\int_{0}^{\frac{π}{4}} 7 tan^{3} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(12x+\sqrt{x)} ?
The derivative of f(x)=sqrt(12x+\sqrt{x)} is (24sqrt(x)+1)/(4sqrt(x)\sqrt{12x+\sqrt{x)}}
What is the first derivative of f(x)=sqrt(12x+\sqrt{x)} ?
The first derivative of f(x)=sqrt(12x+\sqrt{x)} is (24sqrt(x)+1)/(4sqrt(x)\sqrt{12x+\sqrt{x)}}