What is the derivative of 5e^{-x}+e^{3x} ?

The derivative of 5e^{-x}+e^{3x} is -5e^{-x}+e^{3x}*3

What is the first derivative of 5e^{-x}+e^{3x} ?

The first derivative of 5e^{-x}+e^{3x} is -5e^{-x}+e^{3x}*3

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\frac{d}{d x} (5 e^{- x} + e^{3 x})

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

Solution steps

\frac{d}{d x} (5 e^{- x} + e^{3 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 e^{- x}) + \frac{d}{d x} (e^{3 x})

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

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

= - 5 e^{- x} + e^{3 x} \cdot 3

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

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

y = 14 x, y = x^{2}

4 x^{\frac{2}{3}}

\int 6 cos^{5} (x) sin^{4} (x) d x

What is the derivative of 5e^{-x}+e^{3x} ?
The derivative of 5e^{-x}+e^{3x} is -5e^{-x}+e^{3x}*3
What is the first derivative of 5e^{-x}+e^{3x} ?
The first derivative of 5e^{-x}+e^{3x} is -5e^{-x}+e^{3x}*3