At a Glance - Derivative of a Sum (or Difference) of Functions
The derivative of a sum is the sum of the derivatives: (f + g)' = f' + g'.
When the function has more than two terms, and some weird combination of addition and subtraction, the process is similar. We find the derivatives of the individual terms, combine those derivatives by addition or subtraction as in the original function, and everything works out.
Example 1
Let f(x) = sin x + cos x. Find f'(x). |
Example 2
Let f(x) = sin x - cos x. Find f ' (x). |
Example 3
Find the derivative of the polynomial f(x) = 5x^{3 }- 4x^{2}. |
Example 4
Find the derivative of the polynomial f(x) = 6x^{7} + 5x^{4 }- 3x^{2} + 5. |
Exercise 1
Find the derivative of the function.
- f(x) = 3x + 7
Exercise 2
Find the derivative of the function.
- f(x) = e^{x} + ln x
Exercise 3
Find the derivative of the function.
Exercise 4
Find the derivative of the function.
- f(x) = x^{4} - 3x^{2}
Exercise 5
Find the derivative of the function.
Exercise 6
Find the derivative of the function.
- f(x) = log_{2} x^{3} - log_{2} x^{9}
Exercise 7
Find the derivative of the function.
- f(x) = log_{2 }x - 2cos x
Exercise 8
Find the derivative of the function.
- f(x) = 3cos x - 2x^{7} + 4x^{3}
Exercise 9
Find the derivative of the function.
Exercise 10
Find the derivative of the function.
- f(x) = x(x + 4) - (x - 1)^{2}