# What are the rules of derivatives in calculus?

## What are the rules of derivatives in calculus?

Updated table of derivatives

Type of function Form of function Rule
y = constant y = C dy/dx = 0
y = linear function y = ax + b dy/dx = a
y = polynomial of order 2 or higher y = axn + b dy/dx = anxn-1
y = sums or differences of 2 functions y = f(x) + g(x) dy/dx = f'(x) + g'(x).

### What are the rules of derivatives?

Rules for differentiation

• General rule for differentiation:
• The derivative of a constant is equal to zero.
• The derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of the function.
• The derivative of a sum is equal to the sum of the derivatives.

What’s the derivative of 2?

2 is a constant whose value never changes. Thus, the derivative of any constant, such as 2 , is 0 .

Is 2sinx the same as sin2x?

Sin 2x is not the same as 2 sin x. Sine of twice of an angle (x) is equal to twice of sine x cos x.

## What is the formula for derivatives?

Differentiation Formulas List Power Rule: (d/dx) (xn ) = nxn-1 Derivative of a constant, a: (d/dx) (a) = 0 Derivative of a constant multiplied with function f: (d/dx) (a. f) = af’ Sum Rule: (d/dx) (f ± g) = f’ ± g’ Product Rule: (d/dx) (fg) = fg’ + gf’ Quotient Rule: =

### What is a derivative product rule?

Product Rule of Derivatives: In calculus, the product rule in differentiation is a method of finding the derivative of a function that is the multiplication of two other functions for which derivatives exist. This rule was discovered by Gottfried Leibniz , a German Mathematician.

What is derivative rule?

Derivation rule. A method for generating objects, called conclusions of the derivation rule, from a set of objects called the premises of the rule; the formulation of a derivation rule plays a determining role in describing calculi (cf.

What is the general power rule in calculus?

The general power rule is a special case of the chain rule. It is useful when finding the derivative of a function that is raised to the nth power. The general power rule states that this derivative is n times the function raised to the (n-1)th power times the derivative of the function .