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Popular >

derivative of y=(sqrt(x)-10)^{-3}

Solution

derivative of

y = (x - 10)^{- 3}

Solution

- \frac{3}{2 x ( x - 10 ) ^{4}}

Solution steps

\frac{d}{d x} ((x - 10)^{- 3})

Apply the chain rule:

- \frac{3}{( x - 10 ) ^{4}} \frac{d}{d x} (x - 10)

= - \frac{3}{( x - 10 ) ^{4}} \frac{d}{d x} (x - 10)

\frac{d}{d x} (x - 10) = \frac{1}{2 x}

= - \frac{3}{( x - 10 ) ^{4}} \cdot \frac{1}{2 x}

Simplify

- \frac{3}{( x - 10 ) ^{4}} \cdot \frac{1}{2 x} : - \frac{3}{2 x ( x - 10 ) ^{4}}

= - \frac{3}{2 x ( x - 10 ) ^{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of y=(sqrt(x)-10)^{-3} ?
The derivative of y=(sqrt(x)-10)^{-3} is -3/(2sqrt(x)(\sqrt{x)-10)^4}
What is the first derivative of y=(sqrt(x)-10)^{-3} ?
The first derivative of y=(sqrt(x)-10)^{-3} is -3/(2sqrt(x)(\sqrt{x)-10)^4}