What is the derivative of-5/((x-2^2)) ?

The derivative of-5/((x-2^2)) is (10)/((x-2)^3)

What is the first derivative of-5/((x-2^2)) ?

The first derivative of-5/((x-2^2)) is (10)/((x-2)^3)

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\frac{d}{d x} (- \frac{5}{( x - 2 ) ^{2}})

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

Solution steps

\frac{d}{d x} (- \frac{5}{( x - 2 ) ^{2}})

Take the constant out:

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

= - 5 \frac{d}{d x} (\frac{1}{( x - 2 ) ^{2}})

Apply exponent rule:

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

= - 5 \frac{d}{d x} ((x - 2)^{- 2})

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of-5/((x-2^2)) ?
The derivative of-5/((x-2^2)) is (10)/((x-2)^3)
What is the first derivative of-5/((x-2^2)) ?
The first derivative of-5/((x-2^2)) is (10)/((x-2)^3)