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

1 Answer
Jun 23, 2017

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