Question

Hi everyone,

I'm having trouble understanding when to use the product rule and when to use the chain rule.

For example: x(sqroot(x^3-2))
Wouldn't that be solved by product rule? (Answer is by chain rule)

Thanks in advance!

Answer 1

You would use both the product and the chain rules.

Answer 2

Product rule is used when you have some expression times some other expression.

Answer 3

As @Agent47 said, you should use both.

Answer 4

Chain rule is used when you have some function in another function, or some equation to some power.

Answer 5

like Sin(2-x) -> chain rule

Answer 6

x*Sinx -> product rule

Answer 7

x*Sin(2-x) -> both rules

Answer 8

Ohh okay, so in that example I posted above, would "x" be counted as an expression?

Answer 9

yup. You would use the product rule on:
x*sqrt(x^3-2)
and the chain rule on just the sqrt(x^3-2) part

Answer 10

Oh i see, I get it. Lastly could you tell me what makes an expression? Like if there are any properties?

Answer 11

hmmmm well ok let me explain the general case... Product rule is used in finding the derivative of:
f(x)*g(x), and you would have: f(x)*g'(x)+f'(x)*g(x)
However, either f(x) or g(x) could be some more or less complicated expressions, such as sqrt of something, or Sin/Cos, etc of something. So there you would use the chain rule. In your case, g(x)=sqrt(x^3-2), or g(x)=(x^3-2)^(1/2). So to find g'(x) you would have to use the chain rule:
g'(x)=((1/2)*(x^3-2)^(-1/2))*(3x^2)

Answer 12

http://brownsharpie.courtneygibbons.org/?p=90
Might help you to remember when to use a chain rule, you basically use it when u have a function in another function.

Answer 13

Ohh okay I get it, thanks a lot for your help, I really appreciate it.

Answer 14

np