Question

Can anyone please tell me how to differentiate between a chain rule and a power rule ? I don't know which rule to apply when I see a mixed equation

Answer 1

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Answer 2

the power rule is for a single function; the chain rule is for a function inside of a function

Answer 3

f(x) = x^2 ; power rule: 2x

f(g(x)) = sqrt(x^2+1); chain rule: 2x/2sqrt(x^2+1)

Answer 4

whenever you an split the function into nested function; more than one thing happens; you apply the chain rule

Answer 5

yes but sometimes its not easy to see...for example ....(1-7t) to the power of 6, the prof told us to apply chain rule and power rule

Answer 6

the chain rule is what you apply; but the power rule is part of the setup

Answer 7

(1-7t)^6 is a function in a function:

(....)^6 and 1-7t; derive both

Answer 8

6(1-7t)^5 (-7) = -42(1-7t)^5

Answer 9

ok how about sin ( tan square root sinx)

Answer 10

sin(tan(sqrt(sin(x)))) that?

Answer 11

sin(...); tan(....); sqrt(....); sin(.....); x derive it thru now

Answer 12

ok so this is a chain rule I know but the tan and square root of sin x is that a product rule ?

Answer 13

sin(...); tan(....); sqrt(....); sin(.....); x
cos(tan(sqrt(sin(x)))); sec^2(sqrt(sin(x))); 1/2sqrt(sin(x)); cos(x); 1

Answer 14

if you split it out onto like a conveyor belt; you can just derive its parts

Answer 15

and the chain rule says when your done; multiply them all together

Answer 16

\[\frac{cos(tan(\sqrt{sin(x)}))*sec^2(\sqrt{sin(x)})*cos(x)}{2\sqrt{sin(x)}}\]

Answer 17

ok I just want to know what rule u applied inside ( tan square root of sinx)

Answer 18

I understand how u differentiate but I just want to know the rule inside the ( )

Answer 19

the chain rule to split it up; and the only 'power' rule would have been to take care of the sqrt

Answer 20

you have to peel it like an onion; then work on it from the inside out

Answer 21

you cant just pick and choose which ones you do and dont; its all one unit that needs to be accounted for

Answer 22

\[sin(tan(\sqrt{sin(x)}))\]
\[sin(...)*tan(....)*\sqrt{(....)}*sin(....)*x\]
\[cos(...)*sec^2(...)*\frac{1}{2\sqrt{(....)}}*cos(...)*1\]

Answer 23

then you place it all back together like a set of russian dolls

Answer 24

ok got it

Answer 25

thanx a lot

Answer 26

:) youre welcome

Answer 27

I wish u were my prof :)

Thanx again