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Question Number 48501 by peter frank last updated on 24/Nov/18

Answered by Abdulhafeez Abu qatada last updated on 25/Nov/18

$$$$$${\left(\frac{df}{dx}\right)}_y=\sin x(\sin (x+y)\cos y+\cos (x+y)\sin y)$$$${\left(\frac{df}{dx}\right)}_y=\sin x(\sin (x+y)\cos y+\cos (x+y)\sin y)$$$${\left(\frac{df}{dx}\right)}_y=\sin x(\sin (x+y)+\left(y\right))$$$${\left(\frac{df}{dx}\right)}_y=\sin x(\sin (x+2y)$$$$$$$$$$$${\left(\frac{df}{dx}\right)}_x=\sin y(\sin (x+y)\cos x+\cos (x+y)\sin x)$$$${\left(\frac{df}{dx}\right)}_x=\sin y\left(\sin (x+y+\left(x\right))\right)$$$${\left(\frac{df}{dx}\right)}_x=\sin y(\sin (y+2x)$$$$$$$$Abuqatada$$

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