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

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

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

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

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derivative of

y = 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}

\int \frac{x ^{7}}{x ^{4} - 3} d x

(- 7, - 4), (8, 8)

n = 1 \sum \infty \frac{6 ^{n}}{( 4 + 1 1 ^{n} )}

\int \frac{4}{x ^{2} + 25} d x

\frac{6 x}{e ^{x}}

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