what is the chain rule?

Question

anonymous · Answer

What does it mean or what is the formula?

anonymous · Answer

formula

anonymous · Answer

$$\frac{ d }{dx } f(g(x)) = f'(g(x)) * g'(x)$$

anonymous · Answer

Do you have an example or do you want one?

kainui · Answer

The chain rule is usually described as the derivative of the outside times the derivative of the inside.

some examples:

derivative of (2x^2+3x)^3

3(2x^2+3x)^2*(4x+3)

derivative of sin(6x^2)

cos(6x^2)*12x

anonymous · Answer

using the chain rule how do you find $$\int\limits_{3}^{x^2} \sqrt(t^6 +1)$$

anonymous · Answer

You sure this isn't the Fundamental Theory of Calculus?
Is there a dt at the end?

anonymous · Answer

yes there is dt at the end, but it says to use the chain rule to find dy/dx

kainui · Answer

So they want the derivative of this integral then, correct?

anonymous · Answer

yes

kainui · Answer

Check this out: http://mathmistakes.info/facts/CalculusFacts/learn/doi/doi.html

anonymous · Answer

so how do you use the chain rule of sqrt(x^6+1)

kainui · Answer

Sorry I should have sent you this link: http://mathmistakes.info/facts/CalculusFacts/learn/doi/doif.html

anonymous · Answer

its okay, thank you

kainui · Answer

Were you able to get the answer? I think they explain it very well there, but I can clarify any points if you'd like me to. =D