What is the derivative of g(x)=sqrt(x)e^x ?

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

What is the first derivative of g(x)=sqrt(x)e^x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

g (x) = x e^{x}

\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

\int \frac{4}{x ^{2}} - \frac{7}{x ^{5}} d x

f (x) = x^{3} + 7 x - 7, (1, 1)

y^{^{''''}} = 0

y^{^{''}} - 6 y^{^{'}} + 25 y = 64 e^{- t}

\int 2 (x + 2)^{3} d x

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