en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of g(x)=9e^xsqrt(x)

Solution

derivative of

g (x) = 9 e^{x} x

Solution

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

Solution steps

\frac{d}{d x} (9 e^{x} x)

Take the constant out:

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

= 9 \frac{d}{d x} (e^{x} x)

Apply the Product Rule:

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

f = e^{x}, g = x

= 9 (\frac{d}{d x} (e^{x}) x + \frac{d}{d x} (x) e^{x})

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

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

= 9 (e^{x} x + \frac{1}{2 x} e^{x})

\frac{1}{2 x} e^{x} = \frac{e ^{x}}{2 x}

= 9 (e^{x} x + \frac{e ^{x}}{2 x})

Popular Examples

derivative of (x^2/(1+2tan(x)))

\frac{d}{d x} (\frac{x ^{2}}{1 + 2 tan ( x )})

(\partial)/(\partial x)((x-y)/(3xy+2))

\frac{\partial}{\partial x} (\frac{x - y}{3 x y + 2})

integral of (2+ln(x))/(xln(x))

\int \frac{2 + ln ( x )}{x ln ( x )} d x

tangent of y=3x^2+3x tangent of

y = 3 x^{2} + 3 x

integral from 2 to infinity of 9/(x^2)

\int_{2}^{\infty} \frac{9}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of g(x)=9e^xsqrt(x) ?
The derivative of g(x)=9e^xsqrt(x) is 9(e^xsqrt(x)+(e^x)/(2sqrt(x)))
What is the first derivative of g(x)=9e^xsqrt(x) ?
The first derivative of g(x)=9e^xsqrt(x) is 9(e^xsqrt(x)+(e^x)/(2sqrt(x)))