# Answer on Calculus Question for Samantha

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

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

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment