What is the derivative of 3e^{-x}+e^{4x} ?

The derivative of 3e^{-x}+e^{4x} is -3e^{-x}+e^{4x}*4

What is the first derivative of 3e^{-x}+e^{4x} ?

The first derivative of 3e^{-x}+e^{4x} is -3e^{-x}+e^{4x}*4

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derivative of

3 e^{- x} + e^{4 x}

- 3 e^{- x} + e^{4 x} \cdot 4

Solution steps

\frac{d}{d x} (3 e^{- x} + e^{4 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 e^{- x}) + \frac{d}{d x} (e^{4 x})

\frac{d}{d x} (3 e^{- x}) = - 3 e^{- x}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= - 3 e^{- x} + e^{4 x} \cdot 4

\frac{d}{d x} (\frac{4 x + 5}{4 x - 5})

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

\int \frac{6 x}{( 4 - 3 x ^{2} ) ^{4}} d x

\frac{d}{d x} (ln (\frac{x ^{2} + 4}{x ^{2} + 1}))

x^{3} - 6 x^{2} - 15 x + 4

What is the derivative of 3e^{-x}+e^{4x} ?
The derivative of 3e^{-x}+e^{4x} is -3e^{-x}+e^{4x}*4
What is the first derivative of 3e^{-x}+e^{4x} ?
The first derivative of 3e^{-x}+e^{4x} is -3e^{-x}+e^{4x}*4