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

The derivative of-xcos(x-x) is -cos(x)+xsin(x)-1

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

The first derivative of-xcos(x-x) is -cos(x)+xsin(x)-1

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

- cos (x) + x sin (x) - 1

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - (cos (x) - x sin (x)) - 1

Simplify

= - cos (x) + x sin (x) - 1

What is the derivative of-xcos(x-x) ?
The derivative of-xcos(x-x) is -cos(x)+xsin(x)-1
What is the first derivative of-xcos(x-x) ?
The first derivative of-xcos(x-x) is -cos(x)+xsin(x)-1