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Popular >

derivative of f(x)=\sqrt[4]{x^7}

Solution

derivative of

Solution

\frac{7 x ^{6}}{4 ( x ^{7} ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{7})

= \frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \cdot 7 x^{6}

Simplify

\frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \cdot 7 x^{6} : \frac{7 x ^{6}}{4 ( x ^{7} ) ^{\frac{3}{4}}}

= \frac{7 x ^{6}}{4 ( x ^{7} ) ^{\frac{3}{4}}}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=\sqrt[4]{x^7} ?
The derivative of f(x)=\sqrt[4]{x^7} is (7x^6)/(4(x^7)^{3/4)}
What is the first derivative of f(x)=\sqrt[4]{x^7} ?
The first derivative of f(x)=\sqrt[4]{x^7} is (7x^6)/(4(x^7)^{3/4)}