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

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

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

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

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derivative of

y = 2^{- x}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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