What is the derivative of xcos(xsin(x)) ?

The derivative of xcos(xsin(x)) is cos(x)sin(x)+xcos(2x)

What is the first derivative of xcos(xsin(x)) ?

The first derivative of xcos(xsin(x)) is cos(x)sin(x)+xcos(2x)

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

cos (x) sin (x) + x cos (2 x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x) sin (x)

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

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

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

= 1 \cdot cos (x) sin (x) + cos (2 x) x

Simplify

= cos (x) sin (x) + x cos (2 x)

\int \frac{t}{t ^{4} + 7} d t

- x cos (x)

d y = (x + 2 y) d x

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

\frac{\partial}{\partial x} (\frac{x}{( x + y ) ^{2}})

What is the derivative of xcos(xsin(x)) ?
The derivative of xcos(xsin(x)) is cos(x)sin(x)+xcos(2x)
What is the first derivative of xcos(xsin(x)) ?
The first derivative of xcos(xsin(x)) is cos(x)sin(x)+xcos(2x)