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Popular >

derivative of f(x)=\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

derivative of (x^2/(2sqrt(x)+1))

\frac{d}{d x} (\frac{x ^{2}}{2 x + 1})

d/(dy)(x^2-y^2)

\frac{d}{d y} (x^{2} - y^{2})

sum from n=1 to infinity of n/(n^3+2)

n = 1 \sum \infty \frac{n}{n ^{3} + 2}

sum from n=0 to infinity of 1/(2^{n+2)}

n = 0 \sum \infty \frac{1}{2 ^{n + 2}}

integral of (x^2)/((x^2+1)^{3/2)}

\int \frac{x ^{2}}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

Frequently Asked Questions (FAQ)

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