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Popular >

derivative of f(x)=\sqrt[3]{x^5}

Solution

derivative of

Solution

\frac{5 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

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

= \frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \cdot 5 x^{4}

Simplify

\frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \cdot 5 x^{4} : \frac{5 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

= \frac{5 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

Popular Examples

derivative of y= 1/(sqrt(2x-1))derivative of

y = \frac{1}{2 x - 1}

derivative of f(x)=(x^3+5)/(x^2+1)derivative of

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

derivative of arccos(2x^2)

\frac{d}{d x} (arccos (2 x^{2}))

integral of sqrt(2+t^2)

\int 2 + t^{2} d t

integral of 8/(x^2sqrt(x^2+25))

\int \frac{8}{x ^{2} x ^{2} + 25} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=\sqrt[3]{x^5} ?
The derivative of f(x)=\sqrt[3]{x^5} is (5x^4)/(3(x^5)^{2/3)}
What is the first derivative of f(x)=\sqrt[3]{x^5} ?
The first derivative of f(x)=\sqrt[3]{x^5} is (5x^4)/(3(x^5)^{2/3)}