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Popular Calculus >

derivative of f(x)=\sqrt[4]{x^5}

Solution

derivative of

f (x) = 4 x^{5}

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{4 ( x ^{5} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{5})

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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