Here you can find the solution to the exercise problems.This chapter is important for 11th standard.The mastering of this chapter is a must for a student to get good marks.The chapter focuses onDerivative concepts and other related ones as well as the tools that are developed based on the derivatives that are applied in real lifeThe average of a rate is x and if the instance happens over some time.

The averate Rate will remain as x.For example if a student wants to score 90 percent on their exams.He/she has to score higher than 90 in some subjects as he/she might score less than that in other subjects.The average rate of score is the time rate of change of score which is calculated from the total score till now.Any object that moves is the same as any other object.

The runner needs to run at a speed of 20 km/hr.At any point in time the distance travelled is divided by the time taken to calculate the rate of speed.If the runner is at 3 km from the start of the run the speed is 3/6*60 which is 6 minutes.This equates to 30 km/hr.It is not a real measure of rate.

The rate of speed will be around 5.This is the same rate as 60 km/hr.There are four major problems that the mathematicians solve in calculus.In the next section we will see first two details.For a circle the tangent to the circle will cross the border of the circle which will be the same as the circle's radius.

In a curve there are scenarios where the curve only passes through the border once.In the curve there are other occurances where in the tangent can pass through multiple points.The easiest way to determine the tangent of a curve is to find the slope of the line that goes through the two points in the curve.The slope of the curve is determined with the help of the differential quotient.It is divided into two parts called delta y and delta x.

The slope of the curve is also called the slope of the ellipse.The function for calculating the velocity is used.By dividing the change in distance by the change in time it would be simplified.The velocity can be calculated using the position function if we measure time and distance at two points in time.Y is always a function of x according to the logic of differentiating.

We will differentiate y with respect to xThis is how it will result.We will get f'(x) if we differentiate f(exA similar thing can be written as y'.Let's take a look at some examples of differentiating x with y.

There will be 10 x9 when x10 differentiates.There are different willlut in x20 and x19.-4 x-4 will be the result of x-3) differentiating.In -11x-12 differentiating x-11 will have a different effect.Differentiating x1/2 will result in 1/21/2.

When we differentiate y with respect to x we get dy/dx of 10 x9 + 7 x6 + 5 x4 + 3 x2).If we don't differentiate a constant then we won't get anything.Any element other than x is a constant.6x0 when we differentiate we get 6*0*x-1 which will result in zeroA difference of 5 + x3 will result in a difference of 3 x2