Derivative help!?

Question

please take derivative and show steps! thank you, and this is not homework, just review for my math class!

y=sin^4(x/5)

Answer 1

y = sin^4 (x/5)

may look a little scary at first, but then you realise that it's not.

you will be using different differentiating techniques in this problem because you are dealing with a few different things here:

1. the power function: ^4
2. a trigonometric function: sin(x)
3. and a variable term: x/5

rewrite the problem as (sin (x/5))^4. you've made the problem much more simple now.

using the power, chain and quotient rules you will get:

NOTE: i would quickly figure out the derivative of x/5 using the quotient rule and set aside. it is 1/5.

y' = 4 sin^3 (x/5)(cos (x/5)) - cos (x/5)(1/5)
= 4 sin^3 (x/5) - 1/5 cos (x/5)

apart from going to my professor or TA, and my text book just doesn't help me, i use this website to refresh my memory with maths stuff:

http://tutorial.math.lamar.edu/

i hope this helps!

Answer 2

y = sin^4(x/5)

You have 3 functions to deal with:
1) ^4
2) sin(x)
3) x/5

That means you want to progressively take the derivative of the outermost functions, and work your way in. Recall that sin^4(x/5) is the same as [ sin(x/5) ]^4

y = [ sin(x/5) ]^4
y' = 4[ sin(x/5) ]^3 ( cos(x/5) ) (1/5)

Answer 3

d(sin⁴ (x/5))/dx

Use the power and chain rules:

4 sin³ (x/5) d(sin (x/5))dx

Use the chain rule:

4 sin³ (x/5) cos (x/5) d(x/5)dx

And finally:

4/5 sin³ (x/5) cos (x/5)

And we are done.