What is the derivative of 3/((r-2)^2) ?

The derivative of 3/((r-2)^2) is -6/((r-2)^3)

What is the first derivative of 3/((r-2)^2) ?

The first derivative of 3/((r-2)^2) is -6/((r-2)^3)

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derivative of

\frac{3}{( r - 2 ) ^{2}}

- \frac{6}{( r - 2 ) ^{3}}

Solution steps

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

Take the constant out:

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

= 3 \frac{d}{d r} (\frac{1}{( r - 2 ) ^{2}})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 (- \frac{2}{( r - 2 ) ^{3}} \cdot 1) : - \frac{6}{( r - 2 ) ^{3}}

= - \frac{6}{( r - 2 ) ^{3}}

x = 5 + 6 t + 7 t^{2}

\frac{d}{d t} (- 200 t + 9000)

3 x^{\frac{1}{2}} + x^{2}

y = 2 x + cos (x)

y = x (3 - 4 x)

What is the derivative of 3/((r-2)^2) ?
The derivative of 3/((r-2)^2) is -6/((r-2)^3)
What is the first derivative of 3/((r-2)^2) ?
The first derivative of 3/((r-2)^2) is -6/((r-2)^3)