Differentiating both sides of an equation with respect to x to find dxdy
Implicit differentiation is when we differentiate both sides of an equation. It is helpful when we have an equation that cannot be simplified to y=f(x).
For example:
Differentiating both sides with respect to x and using the product rule:
By the chain rule, we know that (y2)′=2y⋅dxdy:
Now collecting dxdy terms:
So
In problems involving implicit derivatives, you may be asked to solve for points where the tangent to the curve is horizontal or vertical. A horizontal tangent means dxdy=0, and a vertical tangent occurs in the case where dxdy=denominatornumerator and the denominator equals zero.
If the question asks for vertical / horizontal normals, just recall that a vertical normal means a horizontal tangent, and vice-versa.
Nice work completing Implicit differentiation, here's a quick recap of what we covered:
Exercises checked off
Differentiating both sides of an equation with respect to x to find dxdy
Implicit differentiation is when we differentiate both sides of an equation. It is helpful when we have an equation that cannot be simplified to y=f(x).
For example:
Differentiating both sides with respect to x and using the product rule:
By the chain rule, we know that (y2)′=2y⋅dxdy:
Now collecting dxdy terms:
So
In problems involving implicit derivatives, you may be asked to solve for points where the tangent to the curve is horizontal or vertical. A horizontal tangent means dxdy=0, and a vertical tangent occurs in the case where dxdy=denominatornumerator and the denominator equals zero.
If the question asks for vertical / horizontal normals, just recall that a vertical normal means a horizontal tangent, and vice-versa.
Nice work completing Implicit differentiation, here's a quick recap of what we covered:
Exercises checked off