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

The derivative of xcos(y-ycos(x)) is cos(y)-xsin(y)(dy)/(dx)-cos(x)(dy)/(dx)+sin(x)y

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

The first derivative of xcos(y-ycos(x)) is cos(y)-xsin(y)(dy)/(dx)-cos(x)(dy)/(dx)+sin(x)y

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

What is the derivative of xcos(y-ycos(x)) ?
The derivative of xcos(y-ycos(x)) is cos(y)-xsin(y)(dy)/(dx)-cos(x)(dy)/(dx)+sin(x)y
What is the first derivative of xcos(y-ycos(x)) ?
The first derivative of xcos(y-ycos(x)) is cos(y)-xsin(y)(dy)/(dx)-cos(x)(dy)/(dx)+sin(x)y