What is the derivative of 125e^{5x} ?

The derivative of 125e^{5x} is 625e^{5x}

What is the first derivative of 125e^{5x} ?

The first derivative of 125e^{5x} is 625e^{5x}

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\frac{d}{d x} (125 e^{5 x})

625 e^{5 x}

Solution steps

\frac{d}{d x} (125 e^{5 x})

Take the constant out:

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

= 125 \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

= 125 e^{5 x} \cdot 5

Simplify

= 625 e^{5 x}

What is the derivative of 125e^{5x} ?
The derivative of 125e^{5x} is 625e^{5x}
What is the first derivative of 125e^{5x} ?
The first derivative of 125e^{5x} is 625e^{5x}