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

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

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

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

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

- x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= - x sin (x)

\int sin (t) cos (n t) d t

y^{^{''}} - 3 y^{^{'}} = e^{3 t}

k = 1 \sum \infty \frac{5 + ( - 2 ) ^{k}}{4 ^{k + 1}}

\int \frac{sin ^{7} ( 12 x )}{cos ^{4} ( 12 x )} d x

f (x) = ln (\frac{7 ( x + 3 )}{x})

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