What is the (sqrt(x)e^x)^' ?

The (sqrt(x)e^x)^' is (e^x)/(2sqrt(x))+e^xsqrt(x)

What is the first (sqrt(x)e^x)^' ?

The first (sqrt(x)e^x)^' is (e^x)/(2sqrt(x))+e^xsqrt(x)

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(x e^{x})^{^{'}}

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

Solution steps

(x e^{x})^{'}

Apply the Product Rule:

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

f = x, g = e^{x}

= (x)^{^{'}} e^{x} + (e^{x})^{^{'}} x

(x)^{'} = \frac{1}{2 x}

(e^{x})^{'} = e^{x}

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

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

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

(e^{x} + y) d x + (e^{y} + x) d y = 0

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

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

\frac{d}{d x} (sin (3 x^{2}) + 2 x^{3})

\frac{\partial}{\partial x} (y e^{\frac{y}{x}})

What is the (sqrt(x)e^x)^' ?
The (sqrt(x)e^x)^' is (e^x)/(2sqrt(x))+e^xsqrt(x)
What is the first (sqrt(x)e^x)^' ?
The first (sqrt(x)e^x)^' is (e^x)/(2sqrt(x))+e^xsqrt(x)