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

The derivative of e^{3x}x is 3e^{3x}x+e^{3x}

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

The first derivative of e^{3x}x is 3e^{3x}x+e^{3x}

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

3 e^{3 x} x + e^{3 x}

Solution steps

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

Apply the Product Rule:

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

f = e^{3 x}, g = x

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

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

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

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

Simplify

= 3 e^{3 x} x + e^{3 x}

\int \frac{I n x}{x} d x

y^{^{'''}} - y^{^{''}} - 8 y^{^{'}} + 12 y = 0

x \frac{d y}{d x} - 2 y = 0

\int 2 x (x^{2} - 9)^{3} d x

\int_{2}^{3} \frac{21}{3 - x} d x

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