What is the derivative of 1/2 x^2e^xln(x) ?

The derivative of 1/2 x^2e^xln(x) is e^xxln(x)+(x(e^xxln(x)+e^x))/2

What is the first derivative of 1/2 x^2e^xln(x) ?

The first derivative of 1/2 x^2e^xln(x) is e^xxln(x)+(x(e^xxln(x)+e^x))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{1}{2} x^{2} e^{x} ln (x))

e^{x} x ln (x) + \frac{x ( e ^{x} x ln ( x ) + e ^{x} )}{2}

Solution steps

\frac{d}{d x} (\frac{1}{2} x^{2} e^{x} ln (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = e^{x} ln (x)

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

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

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

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

Simplify

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

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

f (x) = \frac{cos ( e ^{x} )}{x ^{4} + 1}

2 x, \frac{2 x}{3}

\int \frac{x ^{2} + 1}{x 1 + x ^{4}} d x

\frac{d}{d t} (e^{2 t} cos (2 t))

8 x^{4} ln (6 x)

What is the derivative of 1/2 x^2e^xln(x) ?
The derivative of 1/2 x^2e^xln(x) is e^xxln(x)+(x(e^xxln(x)+e^x))/2
What is the first derivative of 1/2 x^2e^xln(x) ?
The first derivative of 1/2 x^2e^xln(x) is e^xxln(x)+(x(e^xxln(x)+e^x))/2