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Popular >

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

Solution

derivative of

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

sum from n=0 to infinity of n^{3/2}

n = 0 \sum \infty n^{\frac{3}{2}}

sum from n=3 to infinity of (6/11)^{-n}

n = 3 \sum \infty (\frac{6}{11})^{- n}

expand 4x(x^2-9)expand

4 x (x^{2} - 9)

(\partial)/(\partial y)(x(1-x-2y))

\frac{\partial}{\partial y} (x (1 - x - 2 y))

slope ofintercept (0,8),(8,1)slope intercept

(0, 8), (8, 1)

Frequently Asked Questions (FAQ)

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