# Topics of Differential Calculus

In this page, we will cover the topics of differential calculus which includes the derivative of a function, its applications etc. Let us find the topics below.

For two functions f(x) and g(x), by the chain rule, the derivative of the composite function f(g(x)) is given by the following formula:

[f(g(x))]$’$ = f$’$(g(x)) ⋅ g$’$(x)

where $’$ denotes the first order derivative.

Examples of Derivatives by Chain Rule:

The derivative of a function f(x) by first principle is equal to the limit

f$’$(x) = limh→0 $\dfrac{f(x+h)-f(x)}{h}$.

For example, the derivative of x by first principle can be computed as follows:

(x)$’$ = limh→0 $\dfrac{(x+h)- x}{h}$ = limh→0 $\dfrac{h}{h}$ = limh→0 1 = 1.

Derivative of tanx: The derivative tanx is sec2x.

Derivative of e2x: The derivative of e2x is 2e2x.

Derivative of tanx: The derivative tanx is sec2x.

Derivative of e2x: The derivative of e2x is 2e2x.

Derivative of root x: The derivative of square root of x is 1/(2√x).

Derivative of root logx: The derivative of $\sqrt{\log x}$ is

Derivative of root sinx: The derivative of $\sqrt{\sin x}$ is

Derivative of root cosx: The derivative of $\sqrt{\cos x}$ is

Derivative of root ex: The derivative of $\sqrt{e^x}$ is

Derivative of root(x)+1/root(x): The derivative of $\sqrt{x}+\frac{1}{\sqrt{x}}$ is

Derivative of log3x: The derivative of log3x is 1/x.