What is the derivative of (2x-4^{-4}) ?

The derivative of (2x-4^{-4}) is -1/(4(x-2)^5)

What is the first derivative of (2x-4^{-4}) ?

The first derivative of (2x-4^{-4}) is -1/(4(x-2)^5)

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

- \frac{1}{4 ( x - 2 ) ^{5}}

Solution steps

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

Apply the chain rule:

- \frac{4}{( 2 x - 4 ) ^{5}} \frac{d}{d x} (2 x - 4)

= - \frac{4}{( 2 x - 4 ) ^{5}} \frac{d}{d x} (2 x - 4)

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

= - \frac{4}{( 2 x - 4 ) ^{5}} \cdot 2

Simplify

- \frac{4}{( 2 x - 4 ) ^{5}} \cdot 2 : - \frac{1}{4 ( x - 2 ) ^{5}}

= - \frac{1}{4 ( x - 2 ) ^{5}}

\int \frac{1}{( x - 9 ) ( x + 9 )} d x

cos (x) - x sin (x)

\frac{d y}{d x} = 2 x y^{2} + 72 x

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

\frac{d}{d x} (2^{x} + cos (3 x))

What is the derivative of (2x-4^{-4}) ?
The derivative of (2x-4^{-4}) is -1/(4(x-2)^5)
What is the first derivative of (2x-4^{-4}) ?
The first derivative of (2x-4^{-4}) is -1/(4(x-2)^5)