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

The derivative of 2/((x-2^3)) is -6/((x-2)^4)

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

The first derivative of 2/((x-2^3)) is -6/((x-2)^4)

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

- \frac{6}{( x - 2 ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= 2 \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

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

Simplify

2 (- \frac{3}{( x - 2 ) ^{4}} \cdot 1) : - \frac{6}{( x - 2 ) ^{4}}

= - \frac{6}{( x - 2 ) ^{4}}

\frac{\partial}{\partial x} (x^{2} y + 3 x y + y^{2})

x \to \infty lim ((\frac{( 2 x - 3 )}{( 2 x + 5 )})^{2 x + 1})

x = \frac{4}{y}, x = \frac{y}{8}, x = 8 y

\frac{\partial}{\partial x} (\frac{3 x + t}{x - 5 t})

\int_{1}^{2} (8 x^{3} + 3 x^{2}) d x

What is the derivative of 2/((x-2^3)) ?
The derivative of 2/((x-2^3)) is -6/((x-2)^4)
What is the first derivative of 2/((x-2^3)) ?
The first derivative of 2/((x-2^3)) is -6/((x-2)^4)