Question

find the derivative of sin^4 (x)

Answer 1

would it be cos^4x?

Answer 2

i no that the derivative of sin is cos, but the power of 4 confuses me

Answer 3

you can split it up sin^2x * sin^2x than do power reducing

Answer 4

\[\frac{d}{dx}\sin^2 x=4 \sin ^3 x .\cos x\]

Answer 5

sin^4 x sorry

Answer 6

Have you learned about the chain rule yet?

Answer 7

Rewrite it as (cosx)^4

Answer 8

ya i learned the chain rule

Answer 9

Oops (sinx)^4

Answer 10

Just like newone wrote and chain rule it.

Answer 11

so it would be 4sinx^3 * cos?

Answer 12

yes

Answer 13

ok so what happens here is this. you have to use chain rule.

soo....

sin^4(x) --> 4sin^3(x)cos(x)

Answer 14

you can even check it out in wolframalpha

Answer 15

so how do i no when to use the chainrule?

Answer 16

when you have a function inside a function

Answer 17

so for this question sin is the inside function and 4 is the outside?

Answer 18

so we have f(g(x))=(sinx)^4 where f(x)=x^4 and g(x)=sinx

Answer 19

ooooo i c!!

Answer 20

the chain rule is this f'(g(x))*g'(x)

Answer 21

ok. think about it like this. when you find derivative of x^2 its 2x.
we stop right here becuase we note that x is not in any function.

say if we have cos(2x) then we have to use chain rule. becuase x is inside another function. so derivative of cos(2x) = -sin(2x) = so we derivce the function first. and then we note that we have to further derive x. so we derivce 2x = 2. so we get the final answer cos(2x) = -2sin(2x)

chain rule states:

Answer 22

thank u guys!

Answer 23

Let
\[u = (sin\ x) \rightarrow (sin\ x)^4 = u^4\ and\ du/dx = cos\ x\]

Following the chain rule we have
\[d/dx(u^4) = d/du(u^4) * du/dx= 4u^3 * (\cos\ x) = 4(\sin\ x)^3(\cos\ x)\]