How do you implicitly differentiate #5y^2=sin(x)#?

Answer 1

Charles Anctil

It is

#5*2*y*dy/dx=cosx=>dy/dx=cosx/(10*y)#

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Answer 2

Adam Adkins

To implicitly differentiate ( 5y^2 = \sin(x) ), follow these steps:

Differentiate both sides of the equation with respect to ( x ).
Apply the chain rule when differentiating ( \sin(x) ) with respect to ( x ).
Solve for ( \frac{{dy}}{{dx}} ) after differentiation.

After performing these steps, you'll obtain the implicit derivative ( \frac{{dy}}{{dx}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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