Answer to Question #7841 in Calculus for Samantha

Question

Implicit Differentiation of the following:
1.) x sin (5x+4y)=y cos x
2.) dr/dtheta for (theta^(2/7) + r^(2/7))=6
3.) dr/dtheta for (tan(r theta)=1/3

Answer 1

1.
sin(5x+4y)+x cos(5x+4y)*(5+4y')=y'cos x-ysin x
now you need to find expression for y' from above equation

2.
let's denote theta=t
2/7*t^(2/7-1)+2/7*r^(2/7-1)*r'=0
whence r'=-t^(-5/7)/r^(-5/7)
You can find more info about implicit differentiation here