What is the derivative of xsin(1/x) ?

The derivative of xsin(1/x) is sin(1/x)-(cos(1/x))/x

What is the first derivative of xsin(1/x) ?

The first derivative of xsin(1/x) is sin(1/x)-(cos(1/x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x sin (\frac{1}{x})

sin (\frac{1}{x}) - \frac{cos ( \frac{1}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{1}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{1}{x})

= \frac{d x}{d x} sin (\frac{1}{x}) + \frac{d}{d x} (sin (\frac{1}{x})) x

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

\frac{d}{d x} (sin (\frac{1}{x})) = - \frac{cos ( \frac{1}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{1}{x}) + (- \frac{cos ( \frac{1}{x} )}{x ^{2}}) x

Simplify

1 \cdot sin (\frac{1}{x}) + (- \frac{cos ( \frac{1}{x} )}{x ^{2}}) x : sin (\frac{1}{x}) - \frac{cos ( \frac{1}{x} )}{x}

= sin (\frac{1}{x}) - \frac{cos ( \frac{1}{x} )}{x}

\frac{\partial}{\partial y} (y cos (y - 2 x))

\int y e^{2 y} d y

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

n = 0 \sum \infty 2 e^{- n}

\frac{\partial}{\partial x} (9 - x^{2})

What is the derivative of xsin(1/x) ?
The derivative of xsin(1/x) is sin(1/x)-(cos(1/x))/x
What is the first derivative of xsin(1/x) ?
The first derivative of xsin(1/x) is sin(1/x)-(cos(1/x))/x