Find derivative for y=(x^2-4)(x^2+6x-9)?

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Answer 1 · 2018-02-16T08:28:59

#dy/dx=4x^3+18x^2-26x-24#

We want to find the derivative of

#y=(x^2-4)(x^2+6x-9)#

Multiply out the brackets

#y=x^4+6x^3-9x^2-4x^2-24x+36#

#=x^4+6x^3-13x^2-24x+36#

Use the Power Rule, if #color(green)(y=x^n)#

then #color(green)(dy/dx=nx^(n-1))#

Therefore

#dy/dx=4x^(4-1)+3*6x^(3-1)-2*13x^(2-1)-1*24x^(1-1)#

#=4x^3+18x^2-26x-24#