What is the derivative of y=4^{-5x+2} ?

The derivative of y=4^{-5x+2} is -5ln(2)*2^{-10x+5}

What is the first derivative of y=4^{-5x+2} ?

The first derivative of y=4^{-5x+2} is -5ln(2)*2^{-10x+5}

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derivative of

y = 4^{- 5 x + 2}

- 5 ln (2) \cdot 2^{- 10 x + 5}

Solution steps

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

Apply exponent rule:

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

4^{- 5 x + 2} = e^{(- 5 x + 2) l n (4)}

= \frac{d}{d x} (e^{(- 5 x + 2) l n (4)})

Apply the chain rule:

e^{(- 5 x + 2) l n (4)} \frac{d}{d x} ((- 5 x + 2) ln (4))

= e^{(- 5 x + 2) l n (4)} \frac{d}{d x} ((- 5 x + 2) ln (4))

\frac{d}{d x} ((- 5 x + 2) ln (4)) = - 10 ln (2)

= e^{(- 5 x + 2) l n (4)} (- 10 ln (2))

Simplify

e^{(- 5 x + 2) l n (4)} (- 10 ln (2)) : - 5 ln (2) \cdot 2^{- 10 x + 5}

= - 5 ln (2) \cdot 2^{- 10 x + 5}

What is the derivative of y=4^{-5x+2} ?
The derivative of y=4^{-5x+2} is -5ln(2)*2^{-10x+5}
What is the first derivative of y=4^{-5x+2} ?
The first derivative of y=4^{-5x+2} is -5ln(2)*2^{-10x+5}