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Popular >

derivative of 2/(\sqrt[3]{x^2})

Solution

Solution

- \frac{4}{3 x ^{\frac{5}{3}}}

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 2 \frac{d}{d x} ((x^{2})^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{2})

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

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

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

Simplify

2 (- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \cdot 2 x) : - \frac{4}{3 x ^{\frac{5}{3}}}

= - \frac{4}{3 x ^{\frac{5}{3}}}

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d/(dt)((t^2)/(10))

\frac{d}{d t} (\frac{t ^{2}}{10})

tangent of f(x)= 1/(x^3),\at x=5 tangent of

f (x) = \frac{1}{x ^{3}}, at x = 5

integral of (-x+1)/(x^2+4)

\int \frac{- x + 1}{x ^{2} + 4} d x

integral from 2 to infinity of e^{-4p}

\int_{2}^{\infty} e^{- 4 p} d p

integral of (cos(x))/(7-sin(x))

\int \frac{cos ( x )}{7 - sin ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of 2/(\sqrt[3]{x^2}) ?
The derivative of 2/(\sqrt[3]{x^2}) is -4/(3x^{5/3)}
What is the first derivative of 2/(\sqrt[3]{x^2}) ?
The first derivative of 2/(\sqrt[3]{x^2}) is -4/(3x^{5/3)}