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tomocha tomocha
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12 years ago
2x^3 you use the power rule I think
e^-10x why you use the chain rule?
 cos^7 you use chain rule why?
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wrote...
#1
12 years ago
You'd use the power rule for something like 2x^3 because its only a coefficient times a variable with a number being an exponent. So you'd use the power rule for anything that looks like, x^n  and n being a (natural) number.

You would use a chain rule for something that looks like e^x or sin(x) or cos(x) or anything that has a function within a function. So the derivative of these equation would be the derivative of the outer function (keeping the inner function the same) times the derivative of the inner function.

good luck! Wink Face
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#2
12 years ago
You must use the chain rule when whenever the function in question is a composition of functions.

But you know what the interesting thing is? You are actually doing chain rule even when you do the power rule. The power rule is just a generalization of the chain rule to differentiation of monomials raised to a power. For instance:

When you apply chain rule, you multiply the derivative of the inside function by the derivative of the inside function. The inside function in this case is just x

d/dx(2x^3) = (3)(2)x^2(x')

When you differentiate with respect to x, x' is just 1.

d/dx(e^-10x) = (-10x)'e^-10x = -10e^-10x
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