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

The derivative of (10/((x-2)^3)) is -(30)/((x-2)^4)

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

The first derivative of (10/((x-2)^3)) is -(30)/((x-2)^4)

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

- \frac{30}{( x - 2 ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

10 (- \frac{3}{( x - 2 ) ^{4}} \cdot 1) : - \frac{30}{( x - 2 ) ^{4}}

= - \frac{30}{( x - 2 ) ^{4}}

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

\frac{\partial}{\partial x} (6 x + 2 y)

\frac{d}{d z} (\frac{z e ^{i z}}{( z - 2 ) ( z + 1 )})

\int (2 x - 2) e^{- x} d x

\frac{d}{d x} (5 x^{7} e^{x})

What is the derivative of (10/((x-2)^3)) ?
The derivative of (10/((x-2)^3)) is -(30)/((x-2)^4)
What is the first derivative of (10/((x-2)^3)) ?
The first derivative of (10/((x-2)^3)) is -(30)/((x-2)^4)