Fundamental rules for differentiation:
fundamental rules for differentiation
(i) Differentiation of the constant function = 0
i.e. dc/dx = 0;
(ii) Derivative of sum: Let u, v be 2 derivable functions of x so denoting their sum by y, we write, y = u + v
so, ![832_Fundamental rules for differentiation.png](https://www.expertsmind.com/../CMSImages/832_Fundamental rules for differentiation.png)
(iii). Derivative of the difference: Let u, v be 2 derivable function of x, so denoting their difference by y, thus write y = u -v
so, ![688_Fundamental rules for differentiation1.png](https://www.expertsmind.com/../CMSImages/688_Fundamental rules for differentiation1.png)
(iv). Generalisation: By a repeated application of results obtained above, it can be proved that if u1, u2 ......, un be any finite number of the derivable functions, then
y = u1 ± u2 ± u3 ± ....... ± un
![1543_Fundamental rules for differentiation2.png](https://www.expertsmind.com/../CMSImages/1543_Fundamental rules for differentiation2.png)
Example: Find out
.
Solution: Let y = x + 1/x, so let u = x1 and v = 1/x
So y = u + v
![1453_Fundamental rules for differentiation4.png](https://www.expertsmind.com/../CMSImages/1453_Fundamental rules for differentiation4.png)
Example: Find out ![648_Fundamental rules for differentiation5.png](https://www.expertsmind.com/../CMSImages/648_Fundamental rules for differentiation5.png)
Solution: Assume y = x2 - 1/x, so let u = x2 and v = 1/x
So y = u - v
![2425_Fundamental rules for differentiation6.png](https://www.expertsmind.com/CMSImages/2425_Fundamental%20rules%20for%20differentiation6.png)
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