There is a solution to 97 exercise problems in 11th.This is a very important chapter in the standard.If a student wants to get good marks they should master this chapter.A special focus is given to the tools that are developed based on derivatives that are applied in real life in the chapter.The average of a rate is x if an instance happens over time.

The averate rate would remain as x.For example if a student wants to get a perfect score in all subjectsHe/she needs to score higher in some subjects than others as he/she may not score as high in other subjects.The average rate of score is the time rate of change of score which is defined by the total score till now and the number of subjects.Any moving object is subject to the same rules.

A runner could run at a speed of 20 km/h.The rate of speed is divided by distance travelled.If the runner is at 3 km from the start of the run the speed will be 3/6*60 at 6 minutes.This is the same as 30 kilometer/hr.However this isn't a true measure of rate.

The rate of speed will be in the range of 5 to 8.The speed at which this is equal is 60 km/h.Four major problems were solved by mathematicians.In the forthcoming section we will see the first two details.The circle's border will be crossed by the tangent to the circle which will correspond to the radius of the circle.

There are situations where a curve only passes one time through the border of the curve.There are other occurances where the tangent can go through multiple points.The easiest way to figure out the tangent of a curve is to find the slope of the line that goes through two points.To find the slope of the curve Differential quotient is used.It is made up of two parts Delta y and Delta x.

The slope of the curved line is known as the curve slope.The velocity is determined with a position function.The change in distance can be divided by time.It would be simpler to use the position function to calculate the velocity if we measured time and distance at two points in time.The logic of differentiation is that y is always a function of x

We are going to differentiate y with x now.This will lead to dy/DX.We will get f'(x) if we differentiate f(x(x)(xSimilar to dy/dx it can be written as Y'.We should look at a few examples of differentiating y and x.

The difference between x10 and x9 is 10.There are 20 x19 differentiating willlut.-3 x-4 is what the differentiating will result in.In -11x-12 differentiating x-11 will be changed.The result will be 1/2x-1/2 if differentiating x1/2.

10 x9 + 7 x6 + 5 x4 + 3 x2 is what we'll get if we differentiate y with respect to x.If we do not differentiate a constant we will not get any.Any element without x is always unchanging.6x0 when we differentiate we get 6*0*x-1 which results in zero.A difference of 5 x3 will result in 0 x2