What is the derivative of xsin(8/x) ?

The derivative of xsin(8/x) is sin(8/x)-(8cos(8/x))/x

What is the first derivative of xsin(8/x) ?

The first derivative of xsin(8/x) is sin(8/x)-(8cos(8/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{8}{x})

sin (\frac{8}{x}) - \frac{8 cos ( \frac{8}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{8}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{8}{x})

= \frac{d x}{d x} sin (\frac{8}{x}) + \frac{d}{d x} (sin (\frac{8}{x})) x

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

\frac{d}{d x} (sin (\frac{8}{x})) = - \frac{8 cos ( \frac{8}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{8}{x}) + (- \frac{8 cos ( \frac{8}{x} )}{x ^{2}}) x

Simplify

1 \cdot sin (\frac{8}{x}) + (- \frac{8 cos ( \frac{8}{x} )}{x ^{2}}) x : sin (\frac{8}{x}) - \frac{8 cos ( \frac{8}{x} )}{x}

= sin (\frac{8}{x}) - \frac{8 cos ( \frac{8}{x} )}{x}

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

\int \frac{2 x + 5}{( x - 4 ) ( x + 1 )} d x

y = 3 x^{3}

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (t)

\int (3 - 2 x) sin (5 x) d x

What is the derivative of xsin(8/x) ?
The derivative of xsin(8/x) is sin(8/x)-(8cos(8/x))/x
What is the first derivative of xsin(8/x) ?
The first derivative of xsin(8/x) is sin(8/x)-(8cos(8/x))/x