What is the derivative of 3e^{9x} ?

The derivative of 3e^{9x} is 27e^{9x}

What is the first derivative of 3e^{9x} ?

The first derivative of 3e^{9x} is 27e^{9x}

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\frac{d}{d x} (3 e^{9 x})

27 e^{9 x}

Solution steps

\frac{d}{d x} (3 e^{9 x})

Take the constant out:

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

= 3 \frac{d}{d x} (e^{9 x})

Apply the chain rule:

e^{9 x} \frac{d}{d x} (9 x)

= e^{9 x} \frac{d}{d x} (9 x)

\frac{d}{d x} (9 x) = 9

= 3 e^{9 x} \cdot 9

Simplify

= 27 e^{9 x}

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What is the derivative of 3e^{9x} ?
The derivative of 3e^{9x} is 27e^{9x}
What is the first derivative of 3e^{9x} ?
The first derivative of 3e^{9x} is 27e^{9x}