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

The derivative of 3xe^{sqrt(x)} is 3(e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2)

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

The first derivative of 3xe^{sqrt(x)} is 3(e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2)

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

3 (e^{x} + \frac{e ^{x} x}{2})

Solution steps

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

Take the constant out:

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

= 3 \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}

= 3 (\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}

= 3 (1 \cdot e^{x} + \frac{e ^{x}}{2 x} x)

Simplify

3 (1 \cdot e^{x} + \frac{e ^{x}}{2 x} x) : 3 (e^{x} + \frac{e ^{x} x}{2})

= 3 (e^{x} + \frac{e ^{x} x}{2})

What is the derivative of 3xe^{sqrt(x)} ?
The derivative of 3xe^{sqrt(x)} is 3(e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2)
What is the first derivative of 3xe^{sqrt(x)} ?
The first derivative of 3xe^{sqrt(x)} is 3(e^{sqrt(x)}+(e^{sqrt(x)}sqrt(x))/2)