What is the derivative of f(x)=sqrt(x)*e^x ?

The derivative of f(x)=sqrt(x)*e^x is (e^x)/(2sqrt(x))+e^xsqrt(x)

What is the first derivative of f(x)=sqrt(x)*e^x ?

The first derivative of f(x)=sqrt(x)*e^x is (e^x)/(2sqrt(x))+e^xsqrt(x)

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derivative of

f (x) = x \cdot e^{x}

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d 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

f (- 1) = (5 p + 4)^{40}

\int \frac{t}{1 - t} d t

x \to - 3 lim (- 2 x - 3)

x \to 0 lim (\frac{ln ( 1 + x ^{2} )}{x})

What is the derivative of f(x)=sqrt(x)*e^x ?
The derivative of f(x)=sqrt(x)*e^x is (e^x)/(2sqrt(x))+e^xsqrt(x)
What is the first derivative of f(x)=sqrt(x)*e^x ?
The first derivative of f(x)=sqrt(x)*e^x is (e^x)/(2sqrt(x))+e^xsqrt(x)