difference of the der

[ffuh205]

Question 13 of 16 (worth 5 points)
Difference; The derivative of a difference of two functions equals the difference of the derivatives of the two functions.

A. Always false, 100% of the time.

B. Always True, 100% of the time

C. Sometimes true and sometimes not. It depends on the functions.

I know b is false, I'm leaning towards C

 

[BigGlenntheHeavy]

\(\displaystyle You \ know \ B \ is \ false? \ How?\)

\(\displaystyle B \ is \ always \ true, \ I \ think \ we \ are \ dealing \ with \ a \ troll.\)

\(\displaystyle \frac{d}{dx}[f(x)-g(x)] \ = \ f'(x)-g'(x).\)

 

[ffuh205]

Again, marked incorrect for B. That is how I know it is incorrect.

 

[daon]

Simply WRITING f'(x) should imply that the derivative exists. My addendum in the last thread referrs to something like:

\(\displaystyle 0 = [0]' = [\sqrt[3]{x}-\sqrt[3]{x}]' \neq [\sqrt[3]{x}]'-[\sqrt[3]{x}]'\)

For "almost all values" the equality is true, but in general it is not, as the RHS does not make sense for x=0.