What is the derivative of f(x)=xe^{3x} ?

The derivative of f(x)=xe^{3x} is e^{3x}+3e^{3x}x

What is the first derivative of f(x)=xe^{3x} ?

The first derivative of f(x)=xe^{3x} is e^{3x}+3e^{3x}x

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derivative of

f (x) = x e^{3 x}

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

Solution steps

\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}

= \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

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

Simplify

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

\int cos (\frac{nπ x}{l}) d x

x \to 1 lim (4 - x)

\int 4 tan^{3} (x) d x

y^{^{'}} + \frac{6}{5} y = 1 - \frac{1}{6} t

f (x) = (x^{3} - 8)^{\frac{2}{3}}

What is the derivative of f(x)=xe^{3x} ?
The derivative of f(x)=xe^{3x} is e^{3x}+3e^{3x}x
What is the first derivative of f(x)=xe^{3x} ?
The first derivative of f(x)=xe^{3x} is e^{3x}+3e^{3x}x