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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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}

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\frac{d y}{d x} + 3 x^{2} y = 9 x^{2}

\frac{d}{d x} (7 sin^{3} (x))

- \frac{1}{x ^{2} ( sec ^{2} ( y ) )}

\int \frac{( e ^{2 x} + 1 )}{e ^{2 x} - 1} d x

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