What is the derivative of f(3)=-2/((x-2)^2) ?

The derivative of f(3)=-2/((x-2)^2) is 4/((x-2)^3)

What is the first derivative of f(3)=-2/((x-2)^2) ?

The first derivative of f(3)=-2/((x-2)^2) is 4/((x-2)^3)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= - 2 \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

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

Simplify

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

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

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

\frac{\partial}{\partial z} (sin (y) cos (x))

2 x - 17

\int sin (t) - cos (t) d t

What is the derivative of f(3)=-2/((x-2)^2) ?
The derivative of f(3)=-2/((x-2)^2) is 4/((x-2)^3)
What is the first derivative of f(3)=-2/((x-2)^2) ?
The first derivative of f(3)=-2/((x-2)^2) is 4/((x-2)^3)