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

The derivative of axe^{3x} is a(e^{3x}+3e^{3x}x)

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

The first derivative of axe^{3x} is a(e^{3x}+3e^{3x}x)

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

a (e^{3 x} + 3 e^{3 x} x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= a (e^{3 x} + 3 e^{3 x} x)

3 x^{5}

\frac{\partial}{\partial y} (1 + y^{2})

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3}})

\int tan^{11} (x) sec^{8} (x) d x

(2 + x)^{2}

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