What is the derivative of sin(x*cos(x)*1/x) ?

The derivative of sin(x*cos(x)*1/x) is -(cos(x)sin(x)}{x^2}+\frac{cos(2x))/x

What is the first derivative of sin(x*cos(x)*1/x) ?

The first derivative of sin(x*cos(x)*1/x) is -(cos(x)sin(x)}{x^2}+\frac{cos(2x))/x

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\frac{d}{d x} (sin (x) \cdot cos (x) \cdot \frac{1}{x})

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

Solution steps

\frac{d}{d x} (sin (x) cos (x) \frac{1}{x})

Apply the Product Rule:

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

f = sin (x), g = cos (x) \frac{1}{x}

= \frac{d}{d x} (sin (x)) cos (x) \frac{1}{x} + \frac{d}{d x} (cos (x) \frac{1}{x}) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Simplify

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

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

y = 6 x^{2}, y = 4 x^{2}, y = 6 - 5 x

\frac{d}{d x} (2 cos (x) + 2)

\frac{d}{d t} (e^{8 t})

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

\frac{\partial}{\partial x} (e^{x y^{2}} - 2 ln (x) + 3 y)

What is the derivative of sin(x*cos(x)*1/x) ?
The derivative of sin(x*cos(x)*1/x) is -(cos(x)sin(x)}{x^2}+\frac{cos(2x))/x
What is the first derivative of sin(x*cos(x)*1/x) ?
The first derivative of sin(x*cos(x)*1/x) is -(cos(x)sin(x)}{x^2}+\frac{cos(2x))/x