Here you can find the solution to 97 Exercise Problems.There is a very important chapter in 11th standard.If a student wants to get good marks then mastering this chapter is essential.Derivative concepts and related concepts are the focus of the chapter as well as the tools that are developed based on the derivatives that are applied in real life.If the instance happens over a period of time the average of a rate is x.

Then the averate rate will stay the same.A student wants to score 90 percent agreegate score on all subjects.He/she has to score higher in certain subjects as he/she might score lower in other subjects.The time rate of change of score is defined by the number of subjects and is the average rate of score.Any moving object is the same thing.

A runner can run at a speed of 20 km/HR.The distance travelled divided by the time taken is known as the rate of speed.The speed would be 3/6*60 if the runner is 3 km from the start.It's the same as 30km/hr.This is not a good measure of rate.

The average speed is (5-3)/(8-6)*60.60km/HR is the same as this.The following four major problems can be solved by mathematicians.In the upcoming section we will see the first two details.For a circle the tangent to the circle will cross the border of the circle and the radius that goes through it will be the same.

There are situations in which a curve only passes once through the border of the curve.The curve has occurances where the tangent might pass through multiple points.The easiest way to determine the tangent of a curve is to find the slope of the line that passes through the two points.The slope of the curve is found using the differential quotient.It is divided into two parts:Delta y andDelta x.

The slope of the curve is the same as the slope of the line.Using the position function the velocity is calculated.There would be a ration of the change in distance divided by the change in time.It would be simpler to calculate the velocity using the position function if we measured time and distance at two points in time.Y is always a function of x that's the logic of differentiation.

We can differentiate y with respect to x.This will result in a letter d.We will get f'(x) if we differentiate f(X)(x)(xThere is a chance that dy/dx can be written as y'.Let's see a few examples of differentiating y and x.

It will result in 10 x9.The difference between x20 and x19 is called a differentiating willlut.The result is -4 x-4.In -11x-12 differentiating x-11 will be different.A differentiating x1/2 will result in a different number.

When we differentiate y with respect to x we'll get dy/dx of 10 x9 + 7 x6 + 5 x4 + 3 x2If we don't differentiate a constant we won't get anything.Any element that is not x is considered constant.6x0 when we differentiate we get 6*0*x-1 which will result in zero.5 x3 will result in 0 and 3 x2.