# Homework Help: Chain rule!

1. Apr 3, 2009

### ARYT

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

This is confusing. Too many parentheses. We used to solve a composite of two or three functions.

Last edited by a moderator: Nov 29, 2013
2. Apr 3, 2009

### Vagrant

If f(x) = h(g(x)) then f'(x) = h'(g(x)) × g'(x).
In words: differentiate the ‘outside’ function, and then multiply by the derivative of the
‘inside’ function.

Let's take an example,
y= sin (x2)
dy/dx= d(sin x2)/dx *d(x2)/dx

Treat all the parentheses in a similar manner.

Last edited: Apr 3, 2009
3. Apr 3, 2009

### ARYT

I know, I could solve the third one myself, but the first one :(

4. Apr 3, 2009

### Vagrant

Break up the expression as:
z(x) = (1+v(x))5
v(x) = (2-u(x))3
u(x) = (6+7x2)9

finally you have y = 10*z(x)

now dy/dx = dy/dz *dz/dx

Last edited: Apr 3, 2009
5. Apr 3, 2009

### ARYT

(fog(x) )'=g' (x) f' (g(x) )

we have this general rule for two functions only. Give me sth for n functions.

6. Apr 3, 2009

### cristo

Staff Emeritus
shramana has given you a pretty good hint. How about you try to follow it? Post your work, and we will point out any errors.

7. Apr 3, 2009

### Vagrant

Now let's say
g(x)= g(h(x))
so you'll have g'(x)=h'(x)*g'(h(x)) [using f'(x)=g' (x) f' (g(x) )]

substitute the value of g(x) in f'(x) and so on......

8. Apr 3, 2009

### HallsofIvy

Do it step by step: If y= 10u5, the dy/dx= 50u4 du/dx.

And u= 1+v3 so du/dx= 3v^2 dv/dx.

v= ....?

9. Apr 4, 2009

### ARYT

OK. Here I've tried to solve the first one.

Last edited by a moderator: Nov 29, 2013
10. Apr 4, 2009

### ARYT

Although it's too long. I won't be able to do it without a software (for multiplication and things like that). Also, We can't use calculator.

11. Apr 4, 2009

### ARYT

And the second one which compare to the answer given by the Microsoft Math is wrong:

Last edited by a moderator: Nov 29, 2013
12. Apr 4, 2009

### Vagrant

Not at all. You just have to differentiate the functions in the parentheses as you move inwards.

f'(x)=10*z'(x)
z'(x)=5*(1+v(x))4*v'(x)
v'(x)=3*(1-u(x))2*(-u'(x))
u'(x)=9*7*d(x4)/dx

Now substitute the values of u'(x), v'(x),z'(x) and u(x), v(x) in f'(x).

13. Apr 4, 2009

### Vagrant

Step 2 is wrong.
v'(x) = d(ln(ln sec x))/dx