Look at the following table and try to complete it:
| $$f(x)$$ | $$f'(x)$$ |
| $$x+x^2$$ | $$1+2x$$ |
| $$x+3-5x$$ | $$1-5=-4$$ |
| $$2x^9+ 5x$$ | $$18x^8+5$$ |
| $$x-11x^4$$ | $$1-44x^3$$ |
| $$3-\sqrt{x}$$ | $$-\frac{1}{2\sqrt{x}}$$ |
| $$5-x^{-2}$$ | $$2x^{-3}$$ |
| $$g(x)+h(x)$$ | ? |
| $$g(x)-h(x)$$ | ? |
Have you been able to find a general rule for the sum or the difference of two functions? Here is the answer...
The derivative of a sum of functions is the sum of the derivatives of the functions.
Mathematically, if $$$f(x)=g(x) \pm h(x) \Rightarrow f'(x)=g'(x) \pm h'(x) $$$