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Popular >

derivative of f(x)=sqrt(x)e^x

Solution

derivative of

f (x) = x e^{x}

Solution

\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

Popular Examples

tangent of g(x)=x^2-8,\at x=-3 tangent of

g (x) = x^{2} - 8, at x = - 3

derivative of 6x^2+9

\frac{d}{d x} (6 x^{2} + 9)

tangent of f(x)=((2x-1))/((x+5)),\at x=3 tangent of

f (x) = \frac{( 2 x - 1 )}{( x + 5 )}, at x = 3

limit as x approaches 0 of (1+x)^{4/x}

x \to 0 lim ((1 + x)^{\frac{4}{x}})

x^2y^{''}+xy^'+4y=0

x^{2} y^{^{''}} + x y^{^{'}} + 4 y = 0

Frequently Asked Questions (FAQ)

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)