What is the derivative of xsin(6/x) ?

The derivative of xsin(6/x) is sin(6/x)-(6cos(6/x))/x

What is the first derivative of xsin(6/x) ?

The first derivative of xsin(6/x) is sin(6/x)-(6cos(6/x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x sin (\frac{6}{x}))

sin (\frac{6}{x}) - \frac{6 cos ( \frac{6}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{6}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{6}{x})

= \frac{d x}{d x} sin (\frac{6}{x}) + \frac{d}{d x} (sin (\frac{6}{x})) x

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

\frac{d}{d x} (sin (\frac{6}{x})) = - \frac{6 cos ( \frac{6}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{6}{x}) + (- \frac{6 cos ( \frac{6}{x} )}{x ^{2}}) x

Simplify

1 \cdot sin (\frac{6}{x}) + (- \frac{6 cos ( \frac{6}{x} )}{x ^{2}}) x : sin (\frac{6}{x}) - \frac{6 cos ( \frac{6}{x} )}{x}

= sin (\frac{6}{x}) - \frac{6 cos ( \frac{6}{x} )}{x}

\int \frac{x}{( a + b x ^{2} ) ^{3}} d x

y = \frac{x ^{2}}{2} - 3, y = - \frac{x ^{2}}{2} + 2 x

\int_{1}^{9} \frac{1}{x - 7} d x

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

\int \frac{x ^{2}}{x ^{2} - 4 x + 5} d x

What is the derivative of xsin(6/x) ?
The derivative of xsin(6/x) is sin(6/x)-(6cos(6/x))/x
What is the first derivative of xsin(6/x) ?
The first derivative of xsin(6/x) is sin(6/x)-(6cos(6/x))/x