What is the derivative of y= 1/3 e^{3x} ?

The derivative of y= 1/3 e^{3x} is e^{3x}

What is the first derivative of y= 1/3 e^{3x} ?

The first derivative of y= 1/3 e^{3x} is e^{3x}

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derivative of

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

e^{3 x}

Solution steps

\frac{d}{d x} (\frac{1}{3} e^{3 x})

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}

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What is the derivative of y= 1/3 e^{3x} ?
The derivative of y= 1/3 e^{3x} is e^{3x}
What is the first derivative of y= 1/3 e^{3x} ?
The first derivative of y= 1/3 e^{3x} is e^{3x}