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Popular >

derivative of \sqrt[4]{3x^5}

Solution

\frac{d}{d x} (4 3 x^{5})

Solution

\frac{5 \cdot 3 ^{\frac{1}{4}} x ^{\frac{1}{4}}}{4}

Solution steps

\frac{d}{d x} (4 3 x^{5})

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{5}) = 15 x^{4}

= \frac{1}{4 ( 3 x ^{5} ) ^{\frac{3}{4}}} \cdot 15 x^{4}

Simplify

\frac{1}{4 ( 3 x ^{5} ) ^{\frac{3}{4}}} \cdot 15 x^{4} : \frac{5 \cdot 3 ^{\frac{1}{4}} x ^{\frac{1}{4}}}{4}

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[4]{3x^5} ?
The derivative of \sqrt[4]{3x^5} is (5*3^{1/4}x^{1/4})/4
What is the first derivative of \sqrt[4]{3x^5} ?
The first derivative of \sqrt[4]{3x^5} is (5*3^{1/4}x^{1/4})/4