What is the derivative of sin(x-xcos(x)) ?

The derivative of sin(x-xcos(x)) is xsin(x)

What is the first derivative of sin(x-xcos(x)) ?

The first derivative of sin(x-xcos(x)) is xsin(x)

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

x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= cos (x) - (cos (x) - x sin (x))

Simplify

= x sin (x)

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

\frac{d}{d x} (\frac{2}{2 x + 3})

\int \frac{6}{x} d x

\int x^{2} sin (x) d x

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

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