- Inicio
- Derivatives
- Derivative of the sum of two functions
Derivative of the sum of two functions
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 $$f(x)=g(x) \pm h(x) \Rightarrow f'(x)=g'(x) \pm h'(x) $$