Calculus Help!!
1.)Find dy/dx by implicitly differentiating 16y^2-x^2=16

2.) Solve 16y^2-x^2=16 for y, differentiate that equation, and show that you obtain the same answer as for the previous problem.

Question

Calculus Help!!
1.)Find dy/dx by implicitly differentiating 16y^2-x^2=16

2.) Solve 16y^2-x^2=16 for y, differentiate that equation, and show that you obtain the same answer as for the previous problem.

anonymous · Answer

1)
$$32y \frac{ dy }{ dx }-2x=0$$

anonymous · Answer

x2 – y2 = 16
We find the derivative of the left hand side and the right hand side of this relation with respect to x.
The derivative of x2 with respect to x is 
The derivative of y2 with respect to x is 
The derivative of 16 with respect to x is zero. Therefore, we have

We solve this equation to obtain

anonymous · Answer

Thank you!