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ChrisV
 3 years ago
Find the derivative of the funtion.
f(x)=x^2(x2)^4
ChrisV
 3 years ago
Find the derivative of the funtion. f(x)=x^2(x2)^4

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ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=x ^{2}(x2)^{4}\]

.Sam.
 3 years ago
Best ResponseYou've already chosen the best response.2Use product rule, y' = (x^2)(4)(x2)^3+(x2)^4 (2x) \[4x^{2}(x2)^{3}+2x(x2)^{4}\]

.Sam.
 3 years ago
Best ResponseYou've already chosen the best response.2Teach you one technique, y=(left)(right) y'=(copy left)(differentiate right)+(copy right)(differentiate left)

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0you get 2x(x2)^4+x^2(4(x2)^3)

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0then apply the chain rule which i do not understand

.Sam.
 3 years ago
Best ResponseYou've already chosen the best response.2Noneed to use chain rule here.

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0the answer in the back of the book says

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0\[x ^{2}[4(x2)^{3}(1)] + (x2)^{4}(2x) = 2x(x2)^{3}(3x2)\]

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0i dont understand hgow to get to 2x(x2)^3(3x2)

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1f(x)=x^2(x2)^4 split these things up durp, g(x) = x^(2) g'(x) = 2x d(x) = (x2)^4 USE CHAIN RULE!!! s(x) = x^4 s'(x) = 4x^(3) j(x) = x2 j'(x) = 1 so d'(x) =4(x2)^(3)*1 so Now product rule g(x) = x^(2) g'(x) = 2x d(x) = (x2)^4 d'(x) =4(x2)^(3)*1 2x((x2)^4) + (4(x2)^(3))x^(2)

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1f'(x) = 2x((x2)^4) + (4(x2)^(3))x^(2) Best way to deal with derivatives when you are first learning them is to split them into different functions and derive them then put them all together

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1After you do this about a 1,000 times you will be able to do it in your head

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1Any questions? also if you do it in the order I do it you wont mess up using Quotient rule

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0sorry let me read what you wrote

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1Remember Chain rule is just g(x) = x^4 g'(x) = 4x^(3) s(x) = x2 s'(x) = 1 we throw away g(x) and sub s(x) into g'(x) and multiply by s(x) derivative so g'(s(x)) * s'(x)

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1this is the fool proof way of doing derivatives when you first start out at least it was for me

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0ok let me try to reword this

Chlorophyll
 3 years ago
Best ResponseYou've already chosen the best response.0f(x)=x^2(x2)^4 f'(x) = 2x *(x2)^4 + 4x^2 (x 2) ^3 = (x  3) ^3 [ 2x(x2) + 4x^2 ] = (x  3) ^3 [ 6x^2  4x ]

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0(2x)((x+2)^4) + 4x^2(x2)^3

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1g(x)d(x) Take derivative of g(x) take derivative of d(x) you have to use chain rule to do so g'(x)d(x) + g(x)d'(x) if you do it in this order it works for quient rule as well g(x)/d(x) (g'(x)(d(x))  g(x)d'(x))/(d(x))^(2)

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0ah so i then take (2x)((x+2)^4) + 4x^2(x2)^3 and split it like [2x(x+2)^4 +4x^2](x3)^3 ?

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0and do the product rule again?

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1f'(x) = 2x((x2)^4) + (4(x2)^(3))x^(2) That is it you can simplify it but that is the derivative

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1if you wanted to take the second derivative you would use product rule again.

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0ok so i need to simplify f'(x) = 2x((x2)^4) + (4(x2)^(3))x^(2)

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1its only asking for the first derivative so yeah. Is there anything you do not understand about the method I showed you? If you have to you can

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1you can also factor out 2x

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.12x(x2)^(3)(x  2 + 2x)

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0so i would end up with 2x(x2)^3(x2+2x)

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.12x^(1) and x^(1) can be added together

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0you have been so much help

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0i had the right answer the whole time just didnt see the factor

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1because they are to the same power, remember they have to be to the same power to add them you can't add x^(2) + x^(1) or x^(3) + x Not to be partrionizing

cuddlepony
 3 years ago
Best ResponseYou've already chosen the best response.1yeah math can be a hassel sometimes lol
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