# How do you find #dy/dx# by implicit differentiation of #x^2-y^2=16#?

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

To find ( \frac{dy}{dx} ) by implicit differentiation of ( x^2 - y^2 = 16 ), differentiate both sides of the equation with respect to ( x ), treating ( y ) as a function of ( x ) using the chain rule. Then solve for ( \frac{dy}{dx} ).

Differentiating both sides with respect to ( x ), we get:

[ \frac{d}{dx}(x^2) - \frac{d}{dx}(y^2) = \frac{d}{dx}(16) ]

[ 2x - \frac{d}{dx}(y^2) = 0 ]

[ 2x - 2y\frac{dy}{dx} = 0 ]

Now, solve for ( \frac{dy}{dx} ):

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

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

[ \frac{dy}{dx} = \frac{x}{y} ]

Thus, ( \frac{dy}{dx} = \frac{x}{y} ).

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.

- How do you find the derivative of #2/(x+1)#?
- How do you use the chain rule to differentiate #y=8(x^4-x+1)^(3/4)#?
- What is the slope of the tangent line of #(x-y)^3e^y= C #, where C is an arbitrary constant, at #(-2,1)#?
- What is the derivative of #-4/x^2#?
- What is the implicit derivative of #3=(1-y)/x^2+xy #?

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