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Popular >

derivative of 4^{2-2x}

Solution

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

Solution

- ln (2) \cdot 4^{- 2 x + 3}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

4^{2 - 2 x} = e^{(2 - 2 x) l n (4)}

= \frac{d}{d x} (e^{(2 - 2 x) l n (4)})

Apply the chain rule:

e^{(2 - 2 x) l n (4)} \frac{d}{d x} ((2 - 2 x) ln (4))

= e^{(2 - 2 x) l n (4)} \frac{d}{d x} ((2 - 2 x) ln (4))

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

= e^{(2 - 2 x) l n (4)} (- 4 ln (2))

Simplify

e^{(2 - 2 x) l n (4)} (- 4 ln (2)) : - ln (2) \cdot 4^{- 2 x + 3}

= - ln (2) \cdot 4^{- 2 x + 3}

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4

Frequently Asked Questions (FAQ)

What is the derivative of 4^{2-2x} ?
The derivative of 4^{2-2x} is -ln(2)*4^{-2x+3}
What is the first derivative of 4^{2-2x} ?
The first derivative of 4^{2-2x} is -ln(2)*4^{-2x+3}