What is the derivative of f(x)=7e^{-x}-4e^{-7x} ?

The derivative of f(x)=7e^{-x}-4e^{-7x} is -7e^{-x}+28e^{-7x}

What is the first derivative of f(x)=7e^{-x}-4e^{-7x} ?

The first derivative of f(x)=7e^{-x}-4e^{-7x} is -7e^{-x}+28e^{-7x}

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derivative of

f (x) = 7 e^{- x} - 4 e^{- 7 x}

- 7 e^{- x} + 28 e^{- 7 x}

Solution steps

\frac{d}{d x} (7 e^{- x} - 4 e^{- 7 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (7 e^{- x}) - \frac{d}{d x} (4 e^{- 7 x})

\frac{d}{d x} (7 e^{- x}) = - 7 e^{- x}

\frac{d}{d x} (4 e^{- 7 x}) = - 28 e^{- 7 x}

= - 7 e^{- x} - (- 28 e^{- 7 x})

Simplify

= - 7 e^{- x} + 28 e^{- 7 x}

What is the derivative of f(x)=7e^{-x}-4e^{-7x} ?
The derivative of f(x)=7e^{-x}-4e^{-7x} is -7e^{-x}+28e^{-7x}
What is the first derivative of f(x)=7e^{-x}-4e^{-7x} ?
The first derivative of f(x)=7e^{-x}-4e^{-7x} is -7e^{-x}+28e^{-7x}