What is the derivative of xe^{xa} ?

The derivative of xe^{xa} is e^{ax}+ae^{ax}x

What is the first derivative of xe^{xa} ?

The first derivative of xe^{xa} is e^{ax}+ae^{ax}x

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

e^{a x} + a e^{a x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= e^{a x} + a e^{a x} x

x \to \infty lim (- 1^{x} x)

\frac{d}{d x} (4 sin^{5} (x))

\int (1 + \frac{1}{2 x}) d x

\frac{x}{1 + x ^{2}}

\frac{\partial}{\partial y} (sin (x^{2} + x y))

What is the derivative of xe^{xa} ?
The derivative of xe^{xa} is e^{ax}+ae^{ax}x
What is the first derivative of xe^{xa} ?
The first derivative of xe^{xa} is e^{ax}+ae^{ax}x