What is the derivative of f(x)=xsin(2/x) ?

The derivative of f(x)=xsin(2/x) is sin(2/x)-(2cos(2/x))/x

What is the first derivative of f(x)=xsin(2/x) ?

The first derivative of f(x)=xsin(2/x) is sin(2/x)-(2cos(2/x))/x

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derivative of

f (x) = x sin (\frac{2}{x})

sin (\frac{2}{x}) - \frac{2 cos ( \frac{2}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{2}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{2}{x})

= \frac{d x}{d x} sin (\frac{2}{x}) + \frac{d}{d x} (sin (\frac{2}{x})) x

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

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

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

Simplify

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

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

x \to 2 + lim (2 - x^{2})

- \frac{6}{x ^{2}} - \frac{5}{x}

x \to 2 lim (x^{2} - x - 2)

x \to - 2 lim (1)

\int \frac{2 + x ^{2}}{x} d x

What is the derivative of f(x)=xsin(2/x) ?
The derivative of f(x)=xsin(2/x) is sin(2/x)-(2cos(2/x))/x
What is the first derivative of f(x)=xsin(2/x) ?
The first derivative of f(x)=xsin(2/x) is sin(2/x)-(2cos(2/x))/x