What is the derivative of 3ae^{3x} ?

The derivative of 3ae^{3x} is 9ae^{3x}

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

The first derivative of 3ae^{3x} is 9ae^{3x}

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

9 a e^{3 x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x) = 3

= 3 a e^{3 x} \cdot 3

Simplify

= 9 a e^{3 x}

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