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Popular >

derivative of (343+x)^{-1/3}

Solution

derivative of

(343 + x)^{- \frac{1}{3}}

Solution

- \frac{1}{3 ( 343 + x ) ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} ((343 + x)^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( 343 + x ) ^{\frac{4}{3}}} \frac{d}{d x} (343 + x)

= - \frac{1}{3 ( 343 + x ) ^{\frac{4}{3}}} \frac{d}{d x} (343 + x)

\frac{d}{d x} (343 + x) = 1

= - \frac{1}{3 ( 343 + x ) ^{\frac{4}{3}}} \cdot 1

Simplify

= - \frac{1}{3 ( 343 + x ) ^{\frac{4}{3}}}

Popular Examples

derivative of 2x+7

\frac{d}{d x} (2 x + 7)

integral of (x)/(x^2+y^2)

\int \frac{x d y}{x ^{2} + y ^{2}} d x

integral of (2x^3+4x^2+3x-1)/(x^2+2x+1)

\int \frac{2 x ^{3} + 4 x ^{2} + 3 x - 1}{x ^{2} + 2 x + 1} d x

integral of (6-72x)/(sqrt(49-36x^2))

\int \frac{6 - 72 x}{49 - 36 x ^{2}} d x

tangent of f(x)=(x-4)(x^2+8),(1,-27)tangent of

f (x) = (x - 4) (x^{2} + 8), (1, - 27)

Frequently Asked Questions (FAQ)

What is the derivative of (343+x)^{-1/3} ?
The derivative of (343+x)^{-1/3} is -1/(3(343+x)^{4/3)}
What is the first derivative of (343+x)^{-1/3} ?
The first derivative of (343+x)^{-1/3} is -1/(3(343+x)^{4/3)}