Function of a function, Mathematics

Assignment Help:

Function of a Function

Suppose y is a function of z,

           y = f(z)

and z is a function of x,

           z = g(x)

Since, y depends on z, and z in turn depends on x, y is also a function of x.

Thus,  y = f(z)

           = f[g(x)]

The derivative of y with respect to x can be obtained as:

978_function of a function.png

= 2161_function of a function1.png

The above method is often used to get the derivative of some complicated functions.


Related Discussions:- Function of a function

Find the length of the rectangle, Suppose that the width of a rectangle is ...

Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 84 feet. a)    Set up an equation for the perimeter involving

Arithmetic progression., 1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d ar...

1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d are in A.P 2.The nth term of an A.P is an+b.Find the sum of the series upto n terms.

Porportions, how do you solve for porportions?

how do you solve for porportions?

Ratio-categories of situations requiring division , Ratio - situations in ...

Ratio - situations in which we need to compare two quantities in terms of their ratio. (e.g., if Munna weighs 40 Kg. and Munni weighs 50 Kg., find the ratio of their weights.)

Positive real exponents, Simplify following and write the answers with only...

Simplify following and write the answers with only positive exponents.  (a) ( x 8.2 y -0.26 z 2 ) 0.5  (b)  (x 3 y -4.1   / x -2.7 ) -3 Solution  (a) (x 8.2

Find out the domain of function - three dimensional space, Find out the dom...

Find out the domain of each of the following.  (a) f (x,y) = √ (x+y) (b) f (x,y) = √x+√y  (c) f (x,y) = ln (9 - x 2 - 9y 2 ) Solution (a) In this example we know

Determine the range of given algorithm, The division algorithm says that wh...

The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(

Determine the displacement, Example: A 16 lb object stretches a spring 8/9...

Example: A 16 lb object stretches a spring 8/9 ft by itself. Here is no damping as well as no external forces acting on the system. The spring is firstly displaced 6 inches upward

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd