How do you differentiate #f(x)=(x-3)^2+(x-4)^3# using the sum rule?

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Answer 1 · 2017-06-23T03:08:20

You can apply the sum rule right away to the two expressions added.

#d/dx[(x-3)^2+(x-4)^3)]=d/dx[(x-3)^2]+d/dx[(x-4)^3]#

You can then differentiate each part using the chain rule.

#=2(x-3)d/dx(x-3)+3(x-4)^2d/dx(x-4)#

#=2(x-3)(1)+3(x-4)^2(1)" "#The derivative terms go to #1#

#=2x-6+3(x^2-8x+16)" "#Expand the squared term

#=2x-6+3x^2-24x+48" "#Multiply the #3# through

Combining like terms, we get

#=3x^2-22x+42#