# Class 12 Maths Formula for chapter-6 Application of Derivatives

#### Math Formulas

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## Application of Derivative

The derivative is defined as the rate of change of one quantity with respect to another. The rate of change of function is defined as dy/dx = f(x) = y’ in the term of function. The derivative concept is used on a small and large scale. The concept of derivative that are used in many ways such as temperature changes or the rate of change in shape and size of an object depending on the conditions, etc.

### Increasing and Decreasing Functions

Let function f, continuous in [a,b] and differentiable on the open interval (a,b), then

1. f is increasing in [a,b] if f'(x)>0 for each x in (a,b)
2. f is decreasing in [a,b] if f'(x)< 0 for each x in (a,b)
3. f is constant function in [a,b], if f'(x) = 0 for each x in (a,b)

Q1. What is the derivative formula?

Ans. Derivatives are a fundamental tool of calculus. A derivative of a function of a real variable measures the sensitivity to change of a quantity, which is determined by another quantity. Derivative Formula is given as, f 1( x ) = Lim△ x → 0 f ( x + △ x ) − f ( x ) △ x.

Q2. What are the applications of Derivatives?

Ans. Applications of Derivatives in Maths

• Finding Rate of Change of a Quantity.
• Finding the Approximation Value.
• Finding the equation of a Tangent and Normal To a Curve.
• Finding Maxima and Minima, and Point of Inflection.
• Determining Increasing and Decreasing Functions

Q3. What is Derivatives maths class 12?

Ans. The rate of change of a y concerning another x is called the derivative or differential coefficient of y with respect to x.

Q4. What is the limit formula?

Ans. Consider y = f (x) as the function of x. If in point x = a, f (x) takes an indefinite form, then we can consider the values ​​of the function which is closest to a. If these values are inclined to a specific unique number as x tends to, that unique number is called the f (x) limit of x = a.

Q5. How do you solve derivation?

Ans. Following are the steps mentioned below:

• Divide both sides of the equation px2 + qx + r = 0 by p.
• Transpose the quantity c/a to the right side of the equation.
• Complete the square by adding b2 / 4a2 to both sides of the equation.
• Factor the left side and combine the right side.

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