What is the derivative of e^{-x}+1/(e^{8x}) ?

The derivative of e^{-x}+1/(e^{8x}) is -e^{-x}-8e^{-8x}

What is the first derivative of e^{-x}+1/(e^{8x}) ?

The first derivative of e^{-x}+1/(e^{8x}) is -e^{-x}-8e^{-8x}

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\frac{d}{d x} (e^{- x} + \frac{1}{e ^{8 x}})

- e^{- x} - 8 e^{- 8 x}

Solution steps

\frac{d}{d x} (e^{- x} + \frac{1}{e ^{8 x}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{- x}) + \frac{d}{d x} (\frac{1}{e ^{8 x}})

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

\frac{d}{d x} (\frac{1}{e ^{8 x}}) = - 8 e^{- 8 x}

= - e^{- x} - 8 e^{- 8 x}

\int sin (x) cos (cos (x)) d x

\int_{1}^{x^{2}} \frac{1}{t} d t

\int (\frac{x ^{4} - 3 x ^{2} + 5}{x ^{4}}) d x

x^{2} \frac{d y}{d x} - x = 1 + y + x y

f (x) = 12 x

What is the derivative of e^{-x}+1/(e^{8x}) ?
The derivative of e^{-x}+1/(e^{8x}) is -e^{-x}-8e^{-8x}
What is the first derivative of e^{-x}+1/(e^{8x}) ?
The first derivative of e^{-x}+1/(e^{8x}) is -e^{-x}-8e^{-8x}