Sammy K.
asked • 04/15/21Differentiate each function. Express your answer in a simplified factored form
What I did: = 3·1(x + 4)2 (x - 3)6 + (x + 4)3 · 6·1 (x - 3)5
ANSWER: 3(x + 4)2 (x - 3)6 + 6(x + 4)3 (x - 3)5
b) f(x) = sin2(x3- 2x + 4)
This one I would really like help with, please and thank you.
Bradford T. answered • 04/15/21
Retired Engineer / Upper level math instructor
a) Is Correct, but could be simplified with a little algebra.
b) f(x) = sin2(x3-2x+4)
Just remember to employ the chain rule d/dx(sin2(u)) = 2sin(u)cos(u)u'
f'(x) = 2sin(x3-2x+4)cos(x3-2x+4)(3x2-2)
Sammy K.
are the simplified versions correct as well?04/15/21
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Sammy K.
Oh okay thank you so much, for a) a lot of people said it was incorrect so wasn't sure why, but simplified would be 3(x - 3)^5 (x + 4)^2 (3x + 5), right? And for b) the final answer can also be written like 2(3x^2 - 2) cos(x^3 - 2x + 4) sin(x^3 - 2x + 4) or simplified being (6x^2 - 4) cos(x^3 - 2x + 4) sin(x^3 - 2x + 4), is that correct as well?04/15/21