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derivative of 3/(\sqrt[4]{x})

Solution

Solution

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

Solution steps

Take the constant out:

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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