What is the derivative of x*3^x ?

The derivative of x*3^x is 3^x+ln(3)*3^xx

What is the first derivative of x*3^x ?

The first derivative of x*3^x is 3^x+ln(3)*3^xx

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derivative of

x \cdot 3^{x}

3^{x} + ln (3) \cdot 3^{x} x

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 3^{x}

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

\frac{d x}{d x} = 1

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

= 1 \cdot 3^{x} + 3^{x} ln (3) x

Simplify

= 3^{x} + ln (3) \cdot 3^{x} x

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What is the derivative of x*3^x ?
The derivative of x*3^x is 3^x+ln(3)*3^xx
What is the first derivative of x*3^x ?
The first derivative of x*3^x is 3^x+ln(3)*3^xx