What is the derivative of (e^{3x}/3) ?

The derivative of (e^{3x}/3) is e^{3x}

What is the first derivative of (e^{3x}/3) ?

The first derivative of (e^{3x}/3) is e^{3x}

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

e^{3 x}

Solution steps

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

Take the constant out:

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

= \frac{1}{3} \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

= \frac{1}{3} e^{3 x} \cdot 3

Simplify

\frac{1}{3} e^{3 x} \cdot 3 : e^{3 x}

= e^{3 x}

What is the derivative of (e^{3x}/3) ?
The derivative of (e^{3x}/3) is e^{3x}
What is the first derivative of (e^{3x}/3) ?
The first derivative of (e^{3x}/3) is e^{3x}