16 years ago
sxc115

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

in simple easy words...
16 years ago
Sherlock Holmes
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.
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16 years ago
anonymous
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)
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16 years ago
Anonymous
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?
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16 years ago
qwert
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 = â{tanx} you will think of it as â(?) and use the derivative 1/[2â(?)] then you see that ? = tan(x) whose derivative is secÂ² x so that the full answer is dy/dx = {1/[2â(tanx)]} * secÂ² x chain rule can be extended to any number of functions
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16 years ago
sumone^^
y is a function in terms of t, chain rule: dy/dt=(dy/dx)(dx/dt)
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