Here you can find the solution to 97 exercise problems.This is the most important chapter in the 11th standard.It's important for a student to master this chapter in order to get good marks.Special focus is given toDerivative concepts and other related ones in the chapter as well as the tools that are developed based on the derivatives that are applied in real life.If an instance happens over a period of time the average rate is x.

Only the averate rate will not change.For example if a student wants to get a perfect score in all of their subjects.He/she needs to score higher in some subjects as he/she might not score as high in other subjects.The time rate of change of score is determined by the total score and the number of subjects.The same applies to any object that is moving.

A runner is running at a speed of 20 km/hrAt any point in time the measure of rate of speed is the distance travelled divided by the time taken.At 6 minutes the speed is 3/6*60 if the runner is 3 km from the start of the run.This is the same as 30km/HR.This isn't a true measure of rate

Currently the speed is (5-3)/(8-6)*60.60 km/HR is the same as this.Four major problems are solved in calculus by mathematicians.In the coming section we will see the first two in details.The circle's border will be crossed by the tangent to the circle which will be the same as the radius that goes through it.

There are situations where the curve only goes through the border once.There are other occurances where the curve can have multiple points.The easiest way to calculate the curve's tangent is to find the slope of the line that passes through the two points.The slope of the curve is determined with the Differential quotient.It's divided into two parts delta y and delta x.

The slope of a curve is called the slope of the curve.The velocities are calculated using a function.One way to simplify this would be to divide the change in distance by the change in time.It would be easier to calculate the velocity using the position function if we could measure the time and distance at two points in time.The logic of differentiation is that y is always a function of x.

Y and x will be differentiated with respect to x.The result is dy/dx.We will get f'(x) if we differentiate f(X)(x)(xIt is possible to write dy/dx as y'.There are many examples of differentiating y with x.

10 x 9 will be the result of x10 differentiating.There is a difference between x20 and 20 x19.The result is -3 x-4.There is a difference between x-11 and -11x-12.There will be 1/2x1/2 when differentiating x1/2.

When we differentiate y with respect to x we will get dy/x which is 10 x9 + 7 x6 + 5 x4 + 3 x2If we don't differentiate a constant we'll get zero.Any element without x is always the same.6x0 when we differentiate we get 6*0*x-1 which will result in zero.The result will be 0 + 3 x2 if differentiating 5 + x3