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Popular >

derivative of f(x)=\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

integral of 1/(x^2+2x+26)

\int \frac{1}{x ^{2} + 2 x + 26} d x

slope ofintercept (-12,0),(-15,-3)slope intercept

(- 12, 0), (- 15, - 3)

\frac{d y}{d x} = - 2 x y

derivative of 3x^{2/3}-2x derivative of

3 x^{\frac{2}{3}} - 2 x

inverse oflaplace s/(s+10^4)inverse laplace

\frac{s}{s + 1 0 ^{4}}

Frequently Asked Questions (FAQ)

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