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

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

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

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

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

- e^{5 x} \cdot 5

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x) = 5

= - e^{5 x} \cdot 5

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