What is the derivative of y=(-12)/(\sqrt[4]{x)} ?

The derivative of y=(-12)/(\sqrt[4]{x)} is 3/(x^{5/4)}

What is the first derivative of y=(-12)/(\sqrt[4]{x)} ?

The first derivative of y=(-12)/(\sqrt[4]{x)} is 3/(x^{5/4)}

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derivative of

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

Solution steps

Simplify

Take the constant out:

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - 12 \frac{d}{d x} (x^{- \frac{1}{4}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 12 (- \frac{1}{4} x^{- \frac{1}{4} - 1})

Simplify

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

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

What is the derivative of y=(-12)/(\sqrt[4]{x)} ?
The derivative of y=(-12)/(\sqrt[4]{x)} is 3/(x^{5/4)}
What is the first derivative of y=(-12)/(\sqrt[4]{x)} ?
The first derivative of y=(-12)/(\sqrt[4]{x)} is 3/(x^{5/4)}