en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^x(x+xsqrt(x))

Solution

derivative of

e^{x} (x + x x)

Solution

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

Solution steps

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

Simplify

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

= \frac{d}{d x} (e^{x} (x + x^{\frac{3}{2}}))

Apply the Product Rule:

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

f = e^{x}, g = x + x^{\frac{3}{2}}

= \frac{d}{d x} (e^{x}) (x + x^{\frac{3}{2}}) + \frac{d}{d x} (x + x^{\frac{3}{2}}) e^{x}

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

\frac{d}{d x} (x + x^{\frac{3}{2}}) = 1 + \frac{3 x}{2}

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

Graph

Popular Examples

derivative of ln((5x^2+x+6/(x^3)))

\frac{d}{d x} (ln (\frac{5 x ^{2} + x + 6}{x ^{3}}))

integral from 0 to 1 of 12e^{3x}

\int_{0}^{1} 12 e^{3 x} d x

inverse oflaplace s/(s^2+2*3*pi*s+pi^2)inverse laplace

\frac{s}{s ^{2} + 2 \cdot 3 \cdot π \cdot s + π ^{2}}

derivative of (5x+e^x(5-sqrt(x)))

\frac{d}{d x} ((5 x + e^{x}) (5 - x))

d/(dt)(2e^{2t})

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

Frequently Asked Questions (FAQ)

What is the derivative of e^x(x+xsqrt(x)) ?
The derivative of e^x(x+xsqrt(x)) is e^x(x+x^{3/2})+(1+(3sqrt(x))/2)e^x
What is the first derivative of e^x(x+xsqrt(x)) ?
The first derivative of e^x(x+xsqrt(x)) is e^x(x+x^{3/2})+(1+(3sqrt(x))/2)e^x