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Popular >

derivative of (1000+x^{-1/3})

Solution

\frac{d}{d x} ((1000 + x)^{- \frac{1}{3}})

Solution

- \frac{1}{3 ( 1000 + x ) ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} ((1000 + x)^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( 1000 + x ) ^{\frac{4}{3}}} \frac{d}{d x} (1000 + x)

= - \frac{1}{3 ( 1000 + x ) ^{\frac{4}{3}}} \frac{d}{d x} (1000 + x)

\frac{d}{d x} (1000 + x) = 1

= - \frac{1}{3 ( 1000 + x ) ^{\frac{4}{3}}} \cdot 1

Simplify

= - \frac{1}{3 ( 1000 + x ) ^{\frac{4}{3}}}

Popular Examples

integral of csc^2(x)cot^2(x)

\int csc^{2} (x) cot^{2} (x) d x

integral of 6x^2tan(x^3)

\int 6 x^{2} tan (x^{3}) d x

implicit (dy)/(dx),16x^2-16xy+y^2=1 implicit derivative

\frac{d y}{d x}, 16 x^{2} - 16 x y + y^{2} = 1

tangent of f(x)=(x^3-9x)^8,(-3,0)tangent of

f (x) = (x^{3} - 9 x)^{8}, (- 3, 0)

(dy)/(dx)+3y=2x

\frac{d y}{d x} + 3 y = 2 x

Frequently Asked Questions (FAQ)

What is the derivative of (1000+x^{-1/3}) ?
The derivative of (1000+x^{-1/3}) is -1/(3(1000+x)^{4/3)}
What is the first derivative of (1000+x^{-1/3}) ?
The first derivative of (1000+x^{-1/3}) is -1/(3(1000+x)^{4/3)}