What is the derivative of \sqrt[4]{(1/(x^3))} ?

The derivative of \sqrt[4]{(1/(x^3))} is -(3(x^3)^{3/4})/(4x^4)

What is the first derivative of \sqrt[4]{(1/(x^3))} ?

The first derivative of \sqrt[4]{(1/(x^3))} is -(3(x^3)^{3/4})/(4x^4)

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derivative of

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 3 e^{2 t} d t

\int 6 e^{5 x + e^{5 x}} d x

\frac{d}{d y} (- \frac{x}{y})

x \to \infty lim (a x^{2})

\int \frac{3 x}{e ^{x}} d x

What is the derivative of \sqrt[4]{(1/(x^3))} ?
The derivative of \sqrt[4]{(1/(x^3))} is -(3(x^3)^{3/4})/(4x^4)
What is the first derivative of \sqrt[4]{(1/(x^3))} ?
The first derivative of \sqrt[4]{(1/(x^3))} is -(3(x^3)^{3/4})/(4x^4)