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A photo of a Hennessey Venom GT sports car speeding along a winding road.
The Hennessey Venom GT can go from 0 to 200 mph in 14.51 seconds. (credit: modification of work by Codex41, Flickr)

The Hennessey Venom GT is one of the fastest cars in the world. In 2014, it reached a record-setting speed of 270.49 mph. It can go from 0 to 200 mph in 14.51 seconds. The techniques in this chapter can be used to calculate the acceleration the Venom achieves in this feat (see [link] .)

Calculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, and it is critical to analysis in business and health as well. In this chapter, we explore one of the main tools of calculus, the derivative, and show convenient ways to calculate derivatives. We apply these rules to a variety of functions in this chapter so that we can then explore applications of these techniques.

Questions & Answers

find the nth differential coefficient of cosx.cos2x.cos3x
Sudhanayaki Reply
determine the inverse(one-to-one function) of f(x)=x(cube)+4 and draw the graph if the function and its inverse
Crystal Reply
f(x) = x^3 + 4, to find inverse switch x and you and isolate y: x = y^3 + 4 x -4 = y^3 (x-4)^1/3 = y = f^-1(x)
in the example exercise how does it go from -4 +- squareroot(8)/-4 to -4 +- 2squareroot(2)/-4 what is the process of pulling out the factor like that?
Robert Reply
can you please post the question again here so I can see what your talking about
√(8) =√(4x2) =√4 x √2 2 √2 hope this helps. from the surds theory a^c x b^c = (ab)^c
can you determine whether f(x)=x(cube) +4 is a one to one function
one to one means that every input has a single output, and not multiple outputs. whenever the highest power of a given polynomial is odd then that function is said to be odd. a big help to help you understand this concept would be to graph the function and see visually what's going on.
one to one means that every input has a single output, and not multiple outputs. whenever the highest power of a given polynomial is odd then that function is said to be odd. a big help to help you understand this concept would be to graph the function and see visually what's going on.
can you show the steps from going from 3/(x-2)= y to x= 3/y +2 I'm confused as to how y ends up as the divisor
Robert Reply
step 1: take reciprocal of both sides (x-2)/3 = 1/y step 2: multiply both sides by 3 x-2 = 3/y step 3: add 2 to both sides x = 3/y + 2 ps nice farcry 3 background!
first you cross multiply and get y(x-2)=3 then apply distribution and the left side of the equation such as yx-2y=3 then you add 2y in both sides of the equation and get yx=3+2y and last divide both sides of the equation by y and you get x=3/y+2
Multiply both sides by (x-2) to get 3=y(x-2) Then you can divide both sides by y (it's just a multiplied term now) to get 3/y = (x-2). Since the parentheses aren't doing anything for the right side, you can drop them, and add the 2 to both sides to get 3/y + 2 = x
thank you ladies and gentlemen I appreciate the help!
keep practicing and asking questions, practice makes perfect! and be aware that are often different paths to the same answer, so the more you familiarize yourself with these multiple different approaches, the less confused you'll be.
please how do I learn integration
aliyu Reply
they are simply "anti-derivatives". so you should first learn how to take derivatives of any given function before going into taking integrals of any given function.
best way to learn is always to look into a few basic examples of different kinds of functions, and then if you have any further questions, be sure to state specifically which step in the solution you are not understanding.
example 1) say f'(x) = x, f(x) = ? well there is a rule called the 'power rule' which states that if f'(x) = x^n, then f(x) = x^(n+1)/(n+1) so in this case, f(x) = x^2/2
great noticeable direction
limit x tend to infinite xcos(π/2x)*sin(π/4x)
Abhijeet Reply
can you give me a problem for function. a trigonometric one
geovanni Reply
state and prove L hospital rule
Krishna Reply
I want to know about hospital rule
If you tell me how can I Know about engineering math 1( sugh as any lecture or tutorial)
I don't know either i am also new,first year college ,taking computer engineer,and.trying to advance learning
if you want some help on l hospital rule ask me
it's spelled hopital
you are correct Connor Angeli, the L'Hospital was the old one but the modern way to say is L 'Hôpital.
I had no clue this was an online app
Total online shopping during the Christmas holidays has increased dramatically during the past 5 years. In 2012 (t=0), total online holiday sales were $42.3 billion, whereas in 2013 they were $48.1 billion. Find a linear function S that estimates the total online holiday sales in the year t . Interpret the slope of the graph of S . Use part a. to predict the year when online shopping during Christmas will reach $60 billion?
Nguyen Reply
what is the derivative of x= Arc sin (x)^1/2
morfling Reply
y^2 = arcsin(x)
x = sin (y^2)
differentiate implicitly
then solve for dy/dx
thank you it was very helpful
questions solve y=sin x
Obi Reply
Solve it for what?
you have to apply the function arcsin in both sides and you get arcsin y = acrsin (sin x) the the function arcsin and function sin cancel each other so the ecuation becomes arcsin y = x you can also write x= arcsin y
what is the question ? what is the answer?
there is an equation that should be solve for x
ok solve it
are you saying y is of sin(x) y=sin(x)/sin of both sides to solve for x... therefore y/sin =x
or solve for sin(x) via the unit circle
what is unit circle
a circle whose radius is 1.
the unit circle is covered in pre cal...and or trigonometry. it is the multipcation table of upper level mathematics.
what is function?
Ryan Reply
A set of points in which every x value (domain) corresponds to exactly one y value (range)
what is lim (x,y)~(0,0) (x/y)
NIKI Reply
limited of x,y at 0,0 is nt defined
But using L'Hopitals rule is x=1 is defined
Could U explain better boss?
value of (x/y) as (x,y) tends to (0,0) also whats the value of (x+y)/(x^2+y^2) as (x,y) tends to (0,0)
can we apply l hospitals rule for function of two variables
why n does not equal -1
K.kupar Reply
ask a complete question if you want a complete answer.
I agree with Andrew
f (x) = a is a function. It's a constant function.
Darnell Reply

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