What is the derivative of xe^{sqrt(x)} ?

The derivative of xe^{sqrt(x)} is e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2

What is the first derivative of xe^{sqrt(x)} ?

The first derivative of xe^{sqrt(x)} is e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2

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derivative of

x e^{x}

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

\frac{d}{d x} (e^{x}) = \frac{e ^{x}}{2 x}

= 1 \cdot e^{x} + \frac{e ^{x}}{2 x} x

Simplify

1 \cdot e^{x} + \frac{e ^{x}}{2 x} x : e^{x} + \frac{e ^{x} x}{2}

= e^{x} + \frac{e ^{x} x}{2}

f^{^{''''}} = 19 e^{x^{2}}

x \to 0 lim (\frac{1 - x}{x})

\frac{4}{x} + \frac{1}{5 x ^{3} + 2 x}

\frac{d}{d t} (4 cos (π t))

(sin (π))^{^{'}}

What is the derivative of xe^{sqrt(x)} ?
The derivative of xe^{sqrt(x)} is e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2
What is the first derivative of xe^{sqrt(x)} ?
The first derivative of xe^{sqrt(x)} is e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2