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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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