Contents
The chain rule sets the stage for implicit differentiation, which in turn allows us to differentiate inverse functions (and specifically the inverse trigonometric functions). This is really the top of the line when it comes to differentiation.
See how you score on these 20 practice questions

### Implicit differentiation introduction

Some two-variable relationships cannot be turned into a function, like the circle equation x²+y²=4. Implicit differentiation allows us to find the derivative of y with respect to x, even in such equations.

Tackle some more advanced problems of implicit differentiation. For example, find dy/dx for e^(xy²)=x-y.

### Inverse trig functions differentiation

Implicit differentiation allows us to find the derivatives of arcsin(x), arccos(x), and arctan(x).

### Derivatives of inverse functions

Implicit differentiation provides us with the relationship between the derivatives of inverse functions: if f and g are inverse functions, then f’(x)=1/(g’(f(x)). Get comfortable working with this relationship.

### Disguised derivatives

Equipped with knowledge about the derivatives of all common functions, evaluate some limits that represent various derivatives.

### Proofs for the derivatives of eˣ and ln(x)

The derivatives of eˣ and ln(x) may be simple, but proving them is a different story. Learn all about it here.

### Logarithmic differentiation

In logarithmic differentiation, we find the derivative of the natural log of a function instead of the derivative of the function itself. It may surprise you, but this can sometimes actually be easier than regular differentiation, if not the only available option. For example, finding the derivative of xˣ.

### Parametric & vector-valued function differentiation

Parametric and vector-valued functions basically take one input and return two outputs. How do we differentiate such functions? Find out here.