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

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

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