Here you can find the answer to 97 exercise problems.This is an important chapter in 11th standardIt is a must for a student to master this chapter if they want to get good marks.Special focus is given to the tools that are developed based on the derivatives that are applied in real life in the chapter as well as the derivative concepts.If the average of a rate is x and an instance happens over time that's when we know.

Only the averate rate will remain constant.For example a student wants to get a perfect score in all of their subjects.He/she has to score higher than 90% in some subjects as he/she might score lower than 90% in other subjects.The average rate of score is the time rate of change of score which is defined by the total score until now.Any moving object is the same as the other one.

A runner is running at a fast speed.The rate of speed is calculated by dividing distance traveled by time.For 6 minutes the speed would be 3/6*60 if the runner is 3 km from the start of the run.It is equal to 30 km/hrs.This is merely a measure of rate.

The speed at which it will be (5-3)/(8-6)*60) will be the current rate.60 km/hrs is equal.The first four major problems are solved by mathematicians.In the coming section we will see the first couple of details.For a circle the tangent to the circle will cross the border of the circle which is the same as the radius that goes through it.

There are situations where a curve only passes one time through the border.In the curve there are occurances where the tangent may pass through multiple points.The easiest way to find the slope of the line is through two points in the curve.It is possible to find the slope of the curve using Differential quotient.It is divided into two parts: delta y anddelta x.

The slope of the curved line is also known as the curve slope.The position function is used to determine the velocities.The change in distance would be calculated by the change in time.It would be simpler to use the position function to calculate the velocity if we could measure time and distance at two points in time.A function of x is always the logic of differentiation.

The difference between y and x will be determined by respect to x.This will result in a zero.We will get f'(x) if we differentiate f(x)(s)(xThe same can be said for dy/dx.There are examples of differentiating y and x.

There will be 10 x9 for x10 differentiating.The willlut in x20 is different to that in x19.X-2 differentiating will result in x-4.In -11x-12 differentiating x-11 will work.The result of differing x1/2 is 1/2x1/2.

When we differentiate y with respect to x we will get dy/dx of 10 x9 + 7 x6 + 5 x4 + 3 x2).The zero will be obtained if we differentiate a constant.Any element that isn't x is called a constant.We get 6X0 when we differentiate which will result in zero.Differentiating 5 + x3 will result in 3 x2.