Exponentials and logarithms

Exponentials and logarithms

Exponentials and logarithms

The Exponential function
The exponential function is the function whose derivative is equal to its equation. In other words:

Because of this special property, the exponential function is very important in mathematics and crops up frequently.
Like most functions, the exponential has an inverse function, which is ln x (pronounced 'log x').

The Natural Logarithm
ln x is also known as the natural logarithm. The derivative of ln x is 1/x.
It therefore follows that the integral of 1/x is ln x + c .

 

Calculus

Differentiation

Differentiation

Calculus

Differentiation from first principals

Differentiation from first principals

Calculus

Differentiation of trigonometric functions

Differentiation of trigonometric functions

Calculus

Implicit differentiation

Implicit differentiation

Calculus

Integration

Integration

Calculus

Integration by parts

Integration by parts