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

Solution

derivative of

Solution

\frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \cdot 3 x^{2}

Simplify

\frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \cdot 3 x^{2} : \frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{4}}}

= \frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{4}}}

Popular Examples

sum from n=1 to infinity of ((x^n))/(n!)

n = 1 \sum \infty \frac{( x ^{n} )}{n !}

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\int tan^{2} (θ) sec^{4} (θ) d θ

area x^3-3x,x area

x^{3} - 3 x, x

derivative of ln|4x-3|

\frac{d}{d x} (ln ∣ 4 x - 3 ∣)

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[4]{x^3} ?
The derivative of \sqrt[4]{x^3} is (3x^2)/(4(x^3)^{3/4)}
What is the first derivative of \sqrt[4]{x^3} ?
The first derivative of \sqrt[4]{x^3} is (3x^2)/(4(x^3)^{3/4)}