# How do you find #(dy)/(dx)# given #y^2=x#?

OR

By signing up, you agree to our Terms of Service and Privacy Policy

To find ( \frac{{dy}}{{dx}} ) given ( y^2 = x ), you differentiate both sides of the equation with respect to ( x ) using implicit differentiation.

Differentiating both sides:

[ \frac{{d}}{{dx}}(y^2) = \frac{{d}}{{dx}}(x) ]

Using the chain rule for the left side:

[ 2y \frac{{dy}}{{dx}} = 1 ]

Solving for ( \frac{{dy}}{{dx}} ):

[ \frac{{dy}}{{dx}} = \frac{{1}}{{2y}} ]

By signing up, you agree to our Terms of Service and Privacy Policy

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.

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.

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7