What is the derivative of 5e^{-x}+e^{4x} ?

The derivative of 5e^{-x}+e^{4x} is -5e^{-x}+e^{4x}*4

What is the first derivative of 5e^{-x}+e^{4x} ?

The first derivative of 5e^{-x}+e^{4x} is -5e^{-x}+e^{4x}*4

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (5 e^{- x}) = - 5 e^{- x}

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

= - 5 e^{- x} + e^{4 x} \cdot 4

x^{3} y^{^{'''}} - x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = x

\int_{0}^{1} π (x^{2} - x^{6}) d x

t \to 0 lim (\frac{tan ^{2} ( 3 t )}{2 t})

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What is the derivative of 5e^{-x}+e^{4x} ?
The derivative of 5e^{-x}+e^{4x} is -5e^{-x}+e^{4x}*4
What is the first derivative of 5e^{-x}+e^{4x} ?
The first derivative of 5e^{-x}+e^{4x} is -5e^{-x}+e^{4x}*4