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

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

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

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

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derivative of

y = 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

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