Question

taking my AP Calc class was a big mistake. i hate calculus and im usually a math wizard. I DO NOT understand the chain rule at all.... When do i use it? how do i use it? ESPECIALLY with trig functions.. do i add or multiply the derivatives?

example 1) find the derivative
(3x^2)(secx)

example 2) find the derivative
(3xsinx)+(x^2)(cosx)


please tell me why you did what you did on each step. i seriously do not get this at all i seriously need help. i mean i got a 100% on my pre calc exam! why is this so hard for me :( please help thanks!

Answer 1

first one use product rule, power rule for the exponents. There is no chain rule there

Answer 2

Math wizard?

Answer 3

\[
(fg)'=f'g+fg'
\]

Answer 4

1) 6xsecx+3x^2tanxsecx

Answer 5

the second one also doesnt require the chain rule

Answer 6

thank you azbits and wio.

dear azbits, why doesnt the second example require a chain rule? how do i know when to use the chain rule?

Answer 7

first of all, the chain rule.

\[\frac{ d }{ dx }(f\circ g)(x) = f(g(x)) = f'(g(x))\cdot g'(x)\]

Answer 8

2) 3(sinx+xcosx)+(2xcosx-x^2sinx)
all done by product rule and power rule

Answer 9

dear pgpiolet326, is that the basic chain rule formula? because i see stuff with a u' and that throws me off!

Answer 10

dear azbits, how do i do the second example?

Answer 11

you use the chain rule when you need to derive a function inside a function like f'(g(x))
examples
sin(3x^2)+x^2(cos(3x^2)

Answer 12

its so confusing :(

Answer 13

dear azbits,
ohhhh ok so we use the chain rule to avoid crazy steps? what about when i see a square root? when do i use the chain rule for that?

Answer 14

sometimes books, teachers will write u for f(x) and v for g(x).
this is especially true for the product rule.

Answer 15

a simple example is sin(4x)
if you derive that you get 4cos(4x)

Answer 16

same square root = ^1/2

Answer 17

dear pgpilot326, ohhh thats what throws me off thats so stupid when they add the u' :/

Answer 18

ok thank you guys! and how do i know when to use the chain rule with the square root?

Answer 19

savi if you have a square root like (x^2+1)^(1/2) then yes you can use the chain rule

Answer 20

buts if its like sqrt(x) then you can just use the power rule

Answer 21

dear azbits,
is it because of the exponent? or should i use the chain rule everytime i see a square root? lol

Answer 22

\[\frac{ d }{ dx }\sqrt{5x-6}=\frac{ d }{ dx }(5x-6)^{\frac{ 1 }{ 2 }}=\frac{ 1 }{ 2 }(5x-6)^{-\frac{ 1 }{ 2 }}\cdot(5)\]

Answer 23

you should always convert roots to exponents

Answer 24

for derivatives

Answer 25

dear pgpilot326,
ok thanks for the example. but do i ALWAYS use the chain rule with a square root?

Answer 26

no you should only use chain rule when you have a functions that have more than one variable or when the variable doesnt appear by itself

Answer 27

dear azbits,
what does that mean?

Answer 28

yeah. even if it's x inside. look:\[\frac{ d }{ dx }\sqrt{x}=\frac{ d }{ dx }x^{\frac{ 1 }{ 2 }}=x^{-\frac{ 1 }{ 2 }}\cdot(1)=x^{-\frac{ 1 }{ 2 }}\]

Answer 29

@savi56 , try to take a look at this reference. There are some problems here that uses chain rule of differentiation. Try to analyze. This may help you. :) Just try the basics first. I think that will make you understand the rule better.

Answer 30

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html

Answer 31

after a while, you'll learn to recognize

Answer 32

for example a function like f(z)=\[\sqrt{z}\] is too simple to use the chain rule and power rule would be better instead

Answer 33

dear pgpilot,
thank you!

dear Yttrium,
got it in a new tab thank you!

Answer 34

take a look at this
http://tutorial.math.lamar.edu/Classes/CalcI/ChainRule.aspx

Answer 35

dear azbits,
ahhhh i see because its simple. of course if it was the square root of x^2 the answer would be x. if it was the square root of x^3 then you would have to use the chain rule right?

Answer 36

you can use the chain rule on any function...

\[\frac{ d }{ dx }x=\frac{ d }{ dx }x^1=1\cdot x^0 \cdot(1) = 1\]

Answer 37

i see! ok i get it now thank you guys for all your help! ill be back like next week for another question lol!

Answer 38

YA'YA'LL ARE SMART lol. thank you all so much!

Answer 39

well you could muliply the exponents and use power rule but you can use chain rule as well. Point is there is more than one way but some functions require you to use chain rule like the one on that website I linked.

Answer 40

@savi56 if it was (2x-3) inside or (2x^3-3x^2+5) inside.
if it's a pure power, rewrite using exponents and just use power rule.

Answer 41

dear azbits,
alrighty thats true

dear pgpiolet326,
ok because of the big exponents! hahahaha calculus i get you now!

Answer 42

keep at it!

Answer 43

i will lol thanks @azbits and @pgpilot326 !

Answer 44

just practice with more problems and you'll figure it out :).

Answer 45

you're welcome!

Answer 46

yeah im redoing my homework LMAO! night guys thanks!

Answer 47

@azbits i like your profile picture btw :3 Daft Punk!

Answer 48

thanks savi!

Answer 49

np! :)

Answer 50

were up all night to get calculus :D

Answer 51

HAHA i like that xD! were up all night to defeat calculus is how i wud say it :P

Answer 52

wud the derivative of 2x-(x^2)(tanx) by using the chain rule be 2-(2x^3)(tanx)(sec^2)(x)

Answer 53

i just wanna make sure im right

Answer 54

no you have a product in the 2nd term so you'd use the product rule for that.