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Popular Calculus >

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

Solution

derivative of

f (x) = x e^{x} at x

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x} x

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of \sqrt[8]{x}+\sqrt[9]{x}

\int 8 x + 9 x d x

derivative of f(x)=(t^6+1)^{500}

d er i v a t i v e f (x) = (t^{6} + 1)^{500}

tangent of-x/((25-x^2)^{1/2)}

t an g e n t - \frac{x}{( 25 - x ^{2} ) ^{\frac{1}{2}}}

derivative of (125+x)^{-1/3}

d er i v a t i v e (125 + x)^{- \frac{1}{3}}

integral of cos^3(3x)

\int cos^{3} (3 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)e^x\at x ?
The derivative of f(x)=sqrt(x)e^x\at x is (2e^xxsqrt(x)+3e^xsqrt(x))/2
What is the first derivative of f(x)=sqrt(x)e^x\at x ?
The first derivative of f(x)=sqrt(x)e^x\at x is (2e^xxsqrt(x)+3e^xsqrt(x))/2