can anyone explain to me what the CHAIN RULE is?...?

Question

in simple easy words...

Answer 1

If f(x) = g(h(x))

then f ' (x) = g ' (h(x)) * h ' (x)

if g has an inside function of x, then that function is h.
and when u take the derivative, first you take the derivative of outside function only, which is g, and leave inside funtion as it is. After that, you multiply that by the derivative of inside function, which is h.

Answer 2

In calculus, the chain rule is a formula for the derivative of the composite of two functions.

For detailed discussion, see this link.
http://en.wikipedia.org/wiki/Chain_rule

This will be helpful for you to understand cleearly. It also has very good explanation and examples. I too have studied from this and got good idea about the chain rule.

Hope you can clearly understand like me from there.

Answer 3

The derivative of a nested function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. That's as simple as I can say it. You could write it this way:
(f(g(x)))' = f'(g(x))*g'(x)

Answer 4

The chain rule is used to simplify differentiation.

Example: y = 3x^4

dy/dx = 12x^3

Suppose t=x^2, then y = 3t^2, so dy/dt = 6t

But to find dy/dx, we have to find dt/dx:

dt/dx = 2x

So, dy/dx = (dy/dt)*(dt/dx) = 6t*2x

but since t = x^2,

dy/dx = (dy/dt)*(dt/dx) = 6t*2x=6*(x^2)*2x
= 12x^3

Can you see how the chain rule simplifies this sort of differentiation?

Answer 5

if you are differentiating y = sin(ln(x))

you will first think of it as sin (?) and use the derivative cos(?)

then you think of ? = ln(x) whose derivative is (1 / x)

so that the complete answer is dy/dx = cos(ln(x)) * (1 / x)


another example is if you are differentiating y = √{tanx}

you will think of it as √(?) and use the derivative 1/[2√(?)]

then you see that ? = tan(x) whose derivative is sec² x

so that the full answer is dy/dx = {1/[2√(tanx)]} * sec² x

chain rule can be extended to any number of functions

Answer 6

y is a function in terms of t,

chain rule:

dy/dt=(dy/dx)(dx/dt)