What is the derivative of xsin(3/x) ?

The derivative of xsin(3/x) is sin(3/x)-(3cos(3/x))/x

What is the first derivative of xsin(3/x) ?

The first derivative of xsin(3/x) is sin(3/x)-(3cos(3/x))/x

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derivative of

x sin (\frac{3}{x})

sin (\frac{3}{x}) - \frac{3 cos ( \frac{3}{x} )}{x}

Solution steps

\frac{d}{d x} (x sin (\frac{3}{x}))

Apply the Product Rule:

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

f = x, g = sin (\frac{3}{x})

= \frac{d x}{d x} sin (\frac{3}{x}) + \frac{d}{d x} (sin (\frac{3}{x})) x

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

\frac{d}{d x} (sin (\frac{3}{x})) = - \frac{3 cos ( \frac{3}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{3}{x}) + (- \frac{3 cos ( \frac{3}{x} )}{x ^{2}}) x

Simplify

1 \cdot sin (\frac{3}{x}) + (- \frac{3 cos ( \frac{3}{x} )}{x ^{2}}) x : sin (\frac{3}{x}) - \frac{3 cos ( \frac{3}{x} )}{x}

= sin (\frac{3}{x}) - \frac{3 cos ( \frac{3}{x} )}{x}

x \to - 3 lim (\frac{x ^{2} - 9}{3 + x})

\frac{d}{d x} (\frac{2}{3 x ^{\frac{1}{3}}})

\int_{3}^{5} \frac{x}{x ^{2} - 3} d x

(6 x^{2} - 10 x) e^{x}

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

What is the derivative of xsin(3/x) ?
The derivative of xsin(3/x) is sin(3/x)-(3cos(3/x))/x
What is the first derivative of xsin(3/x) ?
The first derivative of xsin(3/x) is sin(3/x)-(3cos(3/x))/x