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Chain rule

Differentiate w.r.t x
(2+x)^3(2-x)^3

i firstly made them into one
so I got
(4-x^2)^6

did the chain rule the long way and got

-12(4-x^2)^5
but the answer when I checked on wolframalpha is

-6x(x^2-4)^2

I think I went wrong with the indices part but not sure why it was wrong :s
Do you mean:

(2+x)3⋅(2−x)3 (2 + x)^3 \cdot (2 - x)^3 because it looks like:

(2+x)3(2−x)3 (2 + x)^{3(2 - x)^{3}}

If it is, then simplifying will give you:

((2+x)⋅(2−x))3=(4−x2)3 ((2 + x) \cdot (2 - x))^3 = (4 - x^2)^3

not to the power of 6.

Remember: (a⋅b)x=ax⋅bx (a\cdot b)^x = a^x \cdot b^x
Reply 2
Avatar for steve2005
steve2005
17
Original post by 0range
Differentiate w.r.t x
(2+x)^3(2-x)^3

i firstly made them into one
so I got
(4-x^2)^6



It should be (4-x^2)^3

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