# Basic Laws of Differentiation

• Scalar multiple rule

Let f (x) and g (x) be any two functions of x. Then,  where, c is any constant

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Solution

=

= 6x
• Sum and difference rule

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Solution

• Product rule

(1st function Ã— 2nd function)

= (1st function Ã— differentiation of 2nd function) + (2nd function Ã— differentiation of 1st function)

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Solution

• Quotient rule

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Solution

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If u and v are two functions of x, then we know that

In the given expression

Example
Solution
If u and v are two functions of x, then we know that

In the given expression

# Derivative of a Function

Let y = f (u), where u = g(x)

Then

Example
Solution
In the given expression