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# Applications of Derivatives in Real Life

Application of Derivative:
Application of Derivative is a part of mathematics relates the change of  one function with respect to another function. Generally the application of derivative is used to measure changes of the system with respect to time. The maximum and minimum range of a function can be determined which helps in graphing of a function without any difficulty.

Application of Derivative in real life :
In everyday day to day we come with application of  derivative.  Some of the application are given below
• Rate of change of displacement
• Rate of change of velocity
• Rate of change of area and volume
• Angle between two curves
• Find the point of curve  at which tangents are parallel to the axis
• To determine tangents and subnormal
Angle between two curves relates angle between  their respective tangents at the point of intersection  (x1,y1)

$\Theta =\tan ^{-1}\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}$

Application of Derivative Problem with Answer:

1. A particle is thrown from a fixed point whose distance is given by S = 2t- 4t -3 units. Find the velocity of the given particle at
t = 3 seconds.

Solution: S = 2t- 4t - 3
Differentiate wit respect to t .

$\frac{dS}{dt}$= 4t - 4

Velocity of the particle  is 4t - 4
Velocity at t = 3
= 4*3 - 4
= 12 - 4
= 8m/sec

2. The volume of the sphere is increasing at 3 c.c per second. Find  the rate of increases of the radius when the radius is 2 cm.

Solution: Given the rate of change of volume of sphere as 3cc/sec

The volume of Sphere = $\frac{4}{3}$ πr3

To find the rate of increases of radius, differentiate volume with respect to t

$\frac{dv}{dt}=\frac{4}{3}3\pi r^{2}\frac{dr}{dt}$

$\frac{dv}{dt}=4\pi r^{2}\frac{dr}{dt}$

3 = $4\pi r^{2}\frac{dr}{dt}$

3 = $4\pi (2)^{2}\frac{dr}{dt}$

$\frac{3}{16\pi }=\frac{dr}{dt}$

The rate of increases of the radius is $\frac{3}{16\pi}$ cm/sec.

3. Find the equation of the tangent to the curve x = et and y = e-t at (1,1)

Solution: Differentiate both the term with respect to t.
x = et     y = e-t

$\frac{dx}{dt}=e^{t}$                $\frac{dy}{dt}=-e^{-t}$

Slope of the tangent is given by $\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{-e^{t}}{e^{t}}=\frac{-y}{x}=-1$

Equation of the tangent :
y -1  = (-1) (x-1)
x + y -2 = 0

Question:This is gonna be an application question on my test. What are some real life applications of the oxidation of alcohols? Alcohols + {O} = (Aldehyde, Ketone, or Carboxylic acid)

Answers:One of the major processes for making formaldehyde commercially is the oxidation of methanol. Formaldehyde is an important industrial chemical used in things like plastics and insulation.

Question:im doing a project on math and i want a subject that will be really interesting. the math needs to be around algebra 2 level, but im having trouble deciding what to do because i have to show the math and how it is used. any help would be appreciated

Answers:Hi, Try conic sections. A parabola is the basis for the satellite dishes that pull in TV signals. They are also the shape of the back of a headlight that focuses the light from the car down the road. An ellipse is a shape they use to build a lithotripter, which is a machine they can use to break up kidney stones for people. A hyperbola relates to hoe air traffic control figures out the locations of airplanes while they're in flight. A circle puts every point on its edge equidistant from the center, something they use in stages built in the round. That's just quickly done off of the top of my head. I also added a website that may be helpful to you!! I hope that helps you!! Good luck!! :-)

Question:Good day! I get 5 points extra credit for up to 4 real life college algebra application papers I write. As an older student (35), I'm fully aware that I won't use most algebra in real life. Thus, I'm stumped. I already have a financial application example and we can only use one of those. I'm looking for exponential growth problems, matrices I might actually use, etc. Simple geometry problems like gallons of paint, volume of my pool, and stuff like that will not be accepted. Thanks for any suggestions! Thanks for your help!

Answers:Algebra is a stepping stone for much more complicated applications. You can't learn to run unless you learn to walk. A great example would be how to maximize the area of an animal pen given an limited amount of fencing. If you have 300 feet of fencing, what is the biggest area you can make? How does the area change if you make the pen 3 sides (build it against a barn or stream) versus four sides. This problem involves calculus, but if one doesn't have the algebra to get to the calculus, this problem would be really hard!

Question:I mean we always talk about only the 1st and the 2nd derivative. I mean we use those two often. But can anyone explain me the real life meaning of the third and fourth derivatives or what actually they represent and helps us to figure out?

Answers:Life it has a meaning and loving purpose - you just have to find your purpose and live it. I believe every person is here for a definite purpose. Each person is special and valuable; that refers to me, you, your family, friends, in fact everybody! There is a loving plan for each of our lives here on earth and there is no such thing as coincidence. I don't believe that anything in life happens by chance and that every aspect of our lives points to something deeper. You need to decide now to live for God rather than for yourself. You spend your life on Earth preparing yourself (as best you can) for death. I don't see death as a scary, negative experience, but birth into a bliss filled eternal life with God. I believe that this is something you have to consciously choose or not during your life on earth. The meaning of life is for us to discover that we are true children of an infinitely loving and merciful God, to find out what our responsibilities are to our Creator, and to fulfill those responsibilities. Each of us is called to affirm, accept and develop the talents God has given us.