What is the derivative of xsin(5/x) ?

The derivative of xsin(5/x) is sin(5/x)-(5cos(5/x))/x

What is the first derivative of xsin(5/x) ?

The first derivative of xsin(5/x) is sin(5/x)-(5cos(5/x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

x sin (\frac{5}{x})

sin (\frac{5}{x}) - \frac{5 cos ( \frac{5}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{5}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{5}{x})

= \frac{d x}{d x} sin (\frac{5}{x}) + \frac{d}{d x} (sin (\frac{5}{x})) x

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

\frac{d}{d x} (sin (\frac{5}{x})) = - \frac{5 cos ( \frac{5}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{5}{x}) + (- \frac{5 cos ( \frac{5}{x} )}{x ^{2}}) x

Simplify

1 \cdot sin (\frac{5}{x}) + (- \frac{5 cos ( \frac{5}{x} )}{x ^{2}}) x : sin (\frac{5}{x}) - \frac{5 cos ( \frac{5}{x} )}{x}

= sin (\frac{5}{x}) - \frac{5 cos ( \frac{5}{x} )}{x}

What is the derivative of xsin(5/x) ?
The derivative of xsin(5/x) is sin(5/x)-(5cos(5/x))/x
What is the first derivative of xsin(5/x) ?
The first derivative of xsin(5/x) is sin(5/x)-(5cos(5/x))/x