Find dy/dx by implicit differentiation.
(sin πx + cos πy)^4 = 67
dy/dx=?

I have a solution here for a slightly similar given which is ((sin(pix)+(cos(piy))^2 = 2. However, if you just analyze the steps and processes in the solution, you might just answer this problem on your own!

You need to remember here that pi is just a number 

so sin(pix) differentiates to to pi*cos(pi*x) 

(cos(pi*y))^2 

the differentiate of this with respect to x goes to 

2(cos(pi*y))* (-pi * sin(pi*y)) * dy/dx 

2 differentiated with respect to x goes to 0 

so you're left with 

piCos(Pi(x)) -2Pi(dy/dx)Sin(Pi(y))Cos(Pi(y)) = 0 

-2Pi(dy/dx)Sin(Pi(y))Cos(Pi(y)) = -piCos(Pi(x)) 

dy/dx = (-piCos(Pi(x))) / -2PiSin(Pi(y))Cos(Pi(y)) 

negatives and pi cancel so 

dy/dx = (Cos(Pi(x))) / 2Sin(Pi(y))Cos(Pi(y))

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