What is the derivative of-xsin(x-cos(x)) ?

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

What is the first derivative of-xsin(x-cos(x)) ?

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

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

- x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

- (sin (x) + x cos (x)) - (- sin (x)) : - x cos (x)

= - x cos (x)

(y e^{4 x y} + x) d x + (x e^{4 x y}) d y = 0

\int sin (x) cos (5 x) d x

x \to 0 lim (x^{a})

\int \frac{1}{6 x ^{3}} d x

\int 18 + 0.5 x d x

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