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Popular >

derivative of y=(2x-5)^{1/3}

Solution

derivative of

y = (2 x - 5)^{\frac{1}{3}}

Solution

\frac{2}{3 ( 2 x - 5 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x - 5) = 2

= \frac{1}{3 ( 2 x - 5 ) ^{\frac{2}{3}}} \cdot 2

Simplify

\frac{1}{3 ( 2 x - 5 ) ^{\frac{2}{3}}} \cdot 2 : \frac{2}{3 ( 2 x - 5 ) ^{\frac{2}{3}}}

= \frac{2}{3 ( 2 x - 5 ) ^{\frac{2}{3}}}

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x \to \infty lim (\frac{4}{x} - 2)

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\int \frac{x}{x ^{4} + 6 x ^{2} + 10} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(2x-5)^{1/3} ?
The derivative of y=(2x-5)^{1/3} is 2/(3(2x-5)^{2/3)}
What is the first derivative of y=(2x-5)^{1/3} ?
The first derivative of y=(2x-5)^{1/3} is 2/(3(2x-5)^{2/3)}