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Popular >

derivative of y=\sqrt[3]{1+5x}

Solution

derivative of

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (5+x+x^2)/(sqrt(x))

\int \frac{5 + x + x ^{2}}{x} d x

integral of (2x+11)/(x^2+4x+5)

\int \frac{2 x + 11}{x ^{2} + 4 x + 5} d x

(\partial)/(\partial x)(8x^2y-3)

\frac{\partial}{\partial x} (8 x^{2} y - 3)

limit as x approaches-2 of-x^2-4x

x \to - 2 lim (- x^{2} - 4 x)

integral from 0 to 1 of (2x)

\int_{0}^{1} (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=\sqrt[3]{1+5x} ?
The derivative of y=\sqrt[3]{1+5x} is 5/(3(1+5x)^{2/3)}
What is the first derivative of y=\sqrt[3]{1+5x} ?
The first derivative of y=\sqrt[3]{1+5x} is 5/(3(1+5x)^{2/3)}