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

The derivative of 5e^{4x} is 20e^{4x}

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

The first derivative of 5e^{4x} is 20e^{4x}

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

20 e^{4 x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x) = 4

= 5 e^{4 x} \cdot 4

Simplify

= 20 e^{4 x}

What is the derivative of 5e^{4x} ?
The derivative of 5e^{4x} is 20e^{4x}
What is the first derivative of 5e^{4x} ?
The first derivative of 5e^{4x} is 20e^{4x}