What is the derivative of x*sin(4/x) ?

The derivative of x*sin(4/x) is sin(4/x)-(4cos(4/x))/x

What is the first derivative of x*sin(4/x) ?

The first derivative of x*sin(4/x) is sin(4/x)-(4cos(4/x))/x

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derivative of

x \cdot 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}

x^{^{''}} - 8 x^{^{'}} + 16 x = 4 t e^{4 t}

\int - cos (4 x) d x

\frac{d}{d x} (7^{x + a r c c o s (x)})

y^{^{''}} + 4 y^{^{'}} + 20 y = 0

\frac{\partial}{\partial x} (0.0099999)

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