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

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

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

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

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derivative of

f (x) = e^{x} x

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

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

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

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

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

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

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