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How do you use the chain rule to differentiate #y=x^3(2x-5)^4#?

1 Answer

Aug 22, 2016

#dy/dx = x^2(2x-5)^3(14x-15)#

Explanation:

#y =x^3(2x-5)^4#

#dy/dx= x^3 * d/dx(2x-5)^4 + (2x-5)^4 * d/dx(x^3)# (Product rule)

#= x^3 * 4(2x-5)^3 * 2 + (2x-5)^4 * 3x^2# (Power rule and Chain rule)

#= x^2(2x-5)^3(8x+3(2x-5))#

#=x^2(2x-5)^3(14x-15)#

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