What is the derivative of (x-1sin(1/(x-1))) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x - 1) = 1

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

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

Simplify

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

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

\frac{\partial}{\partial z} (3 x^{\frac{y}{z}})

e^{x} \frac{( 2 x + 5 ) ^{2}}{x - 2}

y^{^{'}} = - 2 y + x

3 sin^{3} (x)

ln (- 3 x) + 2

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