en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xe^xcot(x)

Solution

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

Solution

e^{x} cot (x) + x (e^{x} cot (x) - e^{x} csc^{2} (x))

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x} cot (x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{x} cot (x)) = e^{x} cot (x) - e^{x} csc^{2} (x)

= 1 \cdot e^{x} cot (x) + (e^{x} cot (x) - e^{x} csc^{2} (x)) x

Simplify

= e^{x} cot (x) + x (e^{x} cot (x) - e^{x} csc^{2} (x))

Popular Examples

derivative of-10x+3cos(x)

\frac{d}{d x} (- 10 x + 3 cos (x))

(d^2)/(dx^2)((2x+5)^7)

\frac{d ^{2}}{d x ^{2}} ((2 x + 5)^{7})

integral from 1 to 4 of (4/x-(16)/(x^2))

\int_{1}^{4} (\frac{4}{x} - \frac{16}{x ^{2}}) d x

(d^2)/(dx^2)(sqrt(r)+\sqrt[6]{r})

(\partial)/(\partial x)((3x+9)/(2-x))

\frac{\partial}{\partial x} (\frac{3 x + 9}{2 - x})

Frequently Asked Questions (FAQ)

What is the derivative of xe^xcot(x) ?
The derivative of xe^xcot(x) is e^xcot(x)+x(e^xcot(x)-e^xcsc^2(x))
What is the first derivative of xe^xcot(x) ?
The first derivative of xe^xcot(x) is e^xcot(x)+x(e^xcot(x)-e^xcsc^2(x))