What is the derivative of f(X)=\sqrt[4]{X^3}-1 ?

The derivative of f(X)=\sqrt[4]{X^3}-1 is (3X^2)/(4(X^3)^{3/4)}

What is the first derivative of f(X)=\sqrt[4]{X^3}-1 ?

The first derivative of f(X)=\sqrt[4]{X^3}-1 is (3X^2)/(4(X^3)^{3/4)}

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derivative of

f (X) = 4 X^{3} - 1

\frac{3 X ^{2}}{4 ( X ^{3} ) ^{\frac{3}{4}}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d X} (4 X^{3}) = \frac{3 X ^{2}}{4 ( X ^{3} ) ^{\frac{3}{4}}}

\frac{d}{d X} (1) = 0

= \frac{3 X ^{2}}{4 ( X ^{3} ) ^{\frac{3}{4}}} - 0

Simplify

= \frac{3 X ^{2}}{4 ( X ^{3} ) ^{\frac{3}{4}}}

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What is the derivative of f(X)=\sqrt[4]{X^3}-1 ?
The derivative of f(X)=\sqrt[4]{X^3}-1 is (3X^2)/(4(X^3)^{3/4)}
What is the first derivative of f(X)=\sqrt[4]{X^3}-1 ?
The first derivative of f(X)=\sqrt[4]{X^3}-1 is (3X^2)/(4(X^3)^{3/4)}