Bobosharif S. answered • 02/10/18
Tutor
4.4
(32)
Mathematics/Statistics Tutor
y=(3x-5)5 (5-x5)4 dy/dx=?
Derivative of product: (uv)=u'v+uv'
Put u=(3x-5)5, v=(5-x5)4, then use chain rule as well.
I'm not sure if (5-x5)4 is written correctly.
Alright, then ( (3x-5)^5 (5-x^5)^4 )'= ((3x-5)^5)' (5-x^5)^4 + (3x-5)^5 ((5-x^5)^4 )'= =15(3x-5)^4(5-x^5)^4-20x^4(3x-5)^5(5-x^5)^3= =5(3x-5)$4(5-x^5)^3(3(x-x^5)-4x^4(3x-5))= =5(3x-5)^4(5-x5)^3(3x-3x^5-12x^5+20x^4)= =5x(3x-5)^4(5-x^5)^3(3+20x^3-15x^4)= You can simplify more if you'd like. Hope it will help you.
Bobosharif S.
Alright, then
( (3x-5)5 (5-x5)4 )'= ((3x-5)5)' (5-x5)4 + (3x-5)5 ((5-x5)4 )'=
=15(3x-5)4(5-x5)4-20x4(3x-5)5(5-x5)3=
=5(3x-5)4(5-x5)3(3(x-x5)-4x4(3x-5))=
=5(3x-5)4(5-x5)3(3x-3x5-12x5+20x4)=
=5x(3x-5)4(5-x5)3(3+20x3-15x4)= You can simplify more if you'd like.
Hope it will help you.
( (3x-5)5 (5-x5)4 )'= ((3x-5)5)' (5-x5)4 + (3x-5)5 ((5-x5)4 )'=
=15(3x-5)4(5-x5)4-20x4(3x-5)5(5-x5)3=
=5(3x-5)4(5-x5)3(3(x-x5)-4x4(3x-5))=
=5(3x-5)4(5-x5)3(3x-3x5-12x5+20x4)=
=5x(3x-5)4(5-x5)3(3+20x3-15x4)= You can simplify more if you'd like.
Hope it will help you.
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02/10/18
Kaylie J.
02/10/18