What is the derivative of 5\sqrt[5]{x^4} ?

The derivative of 5\sqrt[5]{x^4} is 4/(x^{1/5)}

What is the first derivative of 5\sqrt[5]{x^4} ?

The first derivative of 5\sqrt[5]{x^4} is 4/(x^{1/5)}

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\frac{4}{x ^{\frac{1}{5}}}

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{4}{x ^{\frac{1}{5}}}

\int 5 x tan^{2} (x) d x

\int 2 x e^{- 4 x} d x

\int_{0}^{\infty} 7 e^{- x} d x

x \to 0 lim (2 x + 1)

\frac{d}{d x} (\frac{1}{2 x + 12})

What is the derivative of 5\sqrt[5]{x^4} ?
The derivative of 5\sqrt[5]{x^4} is 4/(x^{1/5)}
What is the first derivative of 5\sqrt[5]{x^4} ?
The first derivative of 5\sqrt[5]{x^4} is 4/(x^{1/5)}