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

1 Answer
Andy Y.
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]ddx[(x−3)2+(x−4)3)]=ddx[(x−3)2]+ddx[(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)ddx(x−3)+3(x−4)2ddx(x−4)

=2(x-3)(1)+3(x-4)^2(1)" "=2(x−3)(1)+3(x−4)2(1) The derivative terms go to 11

=2x-6+3(x^2-8x+16)" "=2x−6+3(x2−8x+16) Expand the squared term

=2x-6+3x^2-24x+48" "=2x−6+3x2−24x+48 Multiply the 33 through

Combining like terms, we get

=3x^2-22x+42=3x2−22x+42

Related questions
See all questions in Sum Rule
Impact of this question
2710 views around the world
You can reuse this answer
Creative Commons License