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

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

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

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

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

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

Solution steps

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

Simplify

4^{- 2 x} : 1 6^{- x}

= \frac{d}{d x} (1 6^{- x})

Apply exponent rule:

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

1 6^{- x} = e^{(- x) l n (16)}

= \frac{d}{d x} (e^{(- x) l n (16)})

Apply the chain rule:

e^{(- x) l n (16)} \frac{d}{d x} ((- x) ln (16))

= e^{(- x) l n (16)} \frac{d}{d x} ((- x) ln (16))

\frac{d}{d x} ((- x) ln (16)) = - 4 ln (2)

= e^{(- x) l n (16)} (- 4 ln (2))

Simplify

e^{(- x) l n (16)} (- 4 ln (2)) : - ln (2) \cdot 2^{- 4 x + 2}

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

\frac{d ^{2}}{d x ^{2}} y + 81 y = 0

\frac{d}{d x} (\frac{1 - cosh ( x )}{1 + cosh ( x )})

\int_{0}^{1} x^{2} (x^{3} + 1)^{3} d x

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

1000 \cdot \frac{1}{s ^{2} + 1000 s}

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