Question

I need help with derivatives...

Answer 1

whats your question?

Answer 2

\[y=20\sqrt[5]{x}-\frac{ 3 }{ 4x^2 }\]

Answer 3

do you know the power rule?

Answer 4

sorta.. but, I have a horrible time doing these more complex ones.. im not sure even how to do em... or where to start.

Answer 5

and I really need to learn them.

Answer 6

you can rearrange each of the terms to be in the form ax^n
lets start with the first one
the fifth root of x is actually x^(1/5)
so since the first term is 20 times that, the first term can be written as 20x^(1/5)
right??
use the power rule on this (multiply by the exponent, then subtract 1 from the exponent)

Answer 7

note: the power rule works if any number is the exponent

Answer 8

4x^(-4/5)

Answer 9

yes :)

Answer 10

do u understand why??

Answer 11

yes i do.. except.. are square roots always like that? \[\sqrt[3]{x}\] would be x^(1/3)? what if x was like a number or a number with x...?

Answer 12

yes..
if x has an exponent with it inside the root, that exponent goes in the numerator of the fraction
example:
4th root of x^3 is x^(3/4)

Answer 13

if x is a number, the same rule applies
if theres a number with x, the entire thing gets tthe exponent
example:
7th root of 3x = (3x)^(1/7)

Answer 14

what about sqrt(4x-5)? would be 4x-5^(1/2)?

Answer 15

yes
but be careful with parenthesis
it should be (4x-5)^(1/2)
this is different than 4x-5^(1/2)
in your example, if thats how you wrote it, only the 5 is getting the exponent (the negative sign isnt getting it)
-5^(1/2) is different than (-5)^(1/2)

Answer 16

ohhh okay.. how would the power rule work with (4x-5)^(1/2)= (2x)^(-1/2)?

Answer 17

do you know the chain rule??

Answer 18

A'(B)*B'

Answer 19

oh you would use the chain rule with that because its a function in a function.

Answer 20

yes
so if you have (4x-5)^(1/2)
you multiply by the exponent, subtract one from the exponent, then multiply by the derivative of the inner function
your answer will always have the inner function somewhere inside it (unless of course you simplify)
so on this one, you were close
its really 4*(1/2)(4x-5)^-(1/2)

then you can simplify