Question #7841

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

Expert's answer

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

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

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