Core 4 - Implicit Differentiation

Question 1

Give examples of explicit and implicit functions, and explain how the implicit function differs

Answer 1

Explicit function defines y in terms of the parameter x. e.g. y=2X=4. Given in the form y=f(x)

Implicit functions define y in terms of x and y, e.g. x^2+y^2+4=0

Question 2

What is the method for implicit differentiation of a function?

Answer 2

Differentiate each x function normally, as we are differentiating wrt x, and differential of y wrt x = dy/dx.

Use product rule to differentiate functions like x^2y ==> x^2dy/dx + 2xy

Use chain rule to differentiate trig function e.g. sin(y) ==> dy/dx cos(y).

Question 3

When differentiating a term like (e^3x*y^3), how do you differentiate. What is important to look out for?

Answer 3

Differentiate using product rule, make sure you apply the sign applied to the original function to the two components of the product rule to avoid sign errors.

Question 4

What is the official way to differentiate h=2y^2 wrt x?

Answer 4

By chain rule:

dh/dy=4y
dh/dx=dh/dy*dy/dx=4ydy/dx