What is the solution for -derivative of f(x)=e^{-ax} ?

The solution for -derivative of f(x)=e^{-ax} is f(x)=(e^{-ax})/a+c_{1}

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Find the Derivative - d/dx f(x)=e^(-ax)

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

f (x) = \frac{e ^{- a x}}{a} + c_{1}

Solution steps

- \frac{df}{d x} = e^{- a x}

Isolate

f^{'} (x) : f^{'} (x) = - e^{- a x}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int - e^{- a x} d x

\int - e^{- a x} d x = e^{- a x} \frac{1}{a} + c_{1}

f (x) = e^{- a x} \frac{1}{a} + c_{1}

Simplify

f (x) = \frac{e ^{- a x}}{a} + c_{1}

- \frac{d}{d x} y = cos (2 x)

y = \frac{1}{2 x - 4}

\frac{1}{( 1 - sin ( x ) ) , x}

- \frac{d}{d x} y = 8^{x}

- \frac{d}{d x} (tan (\frac{1}{x}))

What is the solution for -derivative of f(x)=e^{-ax} ?
The solution for -derivative of f(x)=e^{-ax} is f(x)=(e^{-ax})/a+c_{1}