anonymous 4 years ago can someone please explain the chain rule in derivatives?

1. amistre64

when a function relies on another function we have to account for it

2. amistre64

the cahin rule is just saying that the outer function depends on the rate of change of its component function(s)

3. razor99

akshay could u help me

4. amistre64

$f(g(h(x))):f.depends.on.g.which.depends.on.h.which .deoends.on.x$

5. amistre64

f depends on g which depends on h which depends on x

6. amistre64

$\frac{df}{dx}=\frac{df}{dg}\frac{dg}{dh}\frac{dh}{dx}$

7. Akshay_Budhkar

8. anonymous

that's so confusing.. is it possible to get an example please?

9. razor99
10. razor99

this migt help u bro

11. amistre64

if your one a plane thats flying thru the air; and you walk from the back to the front; how fast are you going? well, that all depends on how you compute your speed; and the rate of change depends on not only your speed but the planes speed so we account for both. the chain rule is doing the same thing forrates of change of functions

12. amistre64

sqrt(sin^2(x)-3) 1/2sqrt(sin^2(x)-3) depends on: ()^2 - 3 2(sin(x)) depends on: sin(x) cos(x) depends on x $D_x[\sqrt{sin^2(x)-3}\ ]=\frac{1}{2\sqrt{sin^2(x)-3}}*2(sin(x))*cos(x)$