What is the derivative of y=xsin(4/x) ?

The derivative of y=xsin(4/x) is sin(4/x)-(4cos(4/x))/x

What is the first derivative of y=xsin(4/x) ?

The first derivative of y=xsin(4/x) is sin(4/x)-(4cos(4/x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x sin (\frac{4}{x})

sin (\frac{4}{x}) - \frac{4 cos ( \frac{4}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{4}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{4}{x})

= \frac{d x}{d x} sin (\frac{4}{x}) + \frac{d}{d x} (sin (\frac{4}{x})) x

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

\frac{d}{d x} (sin (\frac{4}{x})) = - \frac{4 cos ( \frac{4}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{4}{x}) + (- \frac{4 cos ( \frac{4}{x} )}{x ^{2}}) x

Simplify

1 \cdot sin (\frac{4}{x}) + (- \frac{4 cos ( \frac{4}{x} )}{x ^{2}}) x : sin (\frac{4}{x}) - \frac{4 cos ( \frac{4}{x} )}{x}

= sin (\frac{4}{x}) - \frac{4 cos ( \frac{4}{x} )}{x}

\int_{1}^{3} (1 + 2 x - 4 x^{3}) d x

\frac{1}{( s ^{2} + 3 s + 2 ) ( s + 1 )}

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

\int \frac{x ^{2} + 4 x - 7}{x - 1} d x

\frac{d}{d x} (\frac{8 x - 1}{6 x + 7})

What is the derivative of y=xsin(4/x) ?
The derivative of y=xsin(4/x) is sin(4/x)-(4cos(4/x))/x
What is the first derivative of y=xsin(4/x) ?
The first derivative of y=xsin(4/x) is sin(4/x)-(4cos(4/x))/x