How do you differentiate #y=(x^4+3)(-4x^5+5x^4+5)# using the product rule?

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How do you differentiate #y=(x^4+3)(-4x^5+5x^4+5)# using the product rule?

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Answer 1 · 2017-04-03T15:35:11

#y'=-4x^3(9x^5-10x^4+15x-20)#

Explanation:

Denote #f(x)=x^4+3# and #g(x)=-4x^5+5x^4+5# so that #y# is of the form #f.g#.

The derivative of #y# with respect to #x# according the product rule is then #f'.g+f.g'#:

#y' =f'.g+f.g'#
#y'=(4x^3)(-4x^5+5x^4+5)+(x^4+3)(-20x^4+20x^3)#
#y'=-16x^8+20x^7+20x^3-20x^8+20x^7-60x^4+60x^3#
#y'=-36x^8+40x^7-60x^4+80x^3#
#y'=-4x^3(9x^5-10x^4+15x-20)#

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How do you differentiate #y=(x^4+3)(-4x^5+5x^4+5)# using the product rule?

1 Answer

Explanation:

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