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

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derivative of

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

\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}

\int 10 t d t

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

2 x \frac{d y}{d x} = 2 x e^{x} - 2 y + 6 x^{2}

\int \frac{1}{3 - 8 x} d x

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