Question

What is the sum rule of derivative?

Answer 1

Hint: Here we know in the given question, we need to express their rule associated with the summation of derivatives, in order to solve it here we will write the standard formulae and then express the result in order to write the solution.

Formulae Used:
\[ \dfrac{d}{{dx}}(x + y) = \dfrac{d}{{dx}}(x) + \dfrac{d}{{dx}}(y)\]

Complete step by step answer:
Here in the given question we know that derivatives, had its own rules and properties on which its works, let start with the simple derivative formulae of a single variable, on solving we get:
\[ \Rightarrow \dfrac{d}{{dx}}(x) = (1){x^{1 - 1}} = 1 \times {x^0} = 1\]
Here now we know that on a simple derivative of any variable, the power to the variable will multiply with the result as coefficient and the power will also be reduced by one.
Now here we need to write the rule for sum, on solving we get:
\[ \Rightarrow \dfrac{d}{{dx}}(x + y) = \dfrac{d}{{dx}}(x) + \dfrac{d}{{dx}}(y)\]
Here we get the rule for derivative, here we can see that derivative will split with every term if they are in sum, if the given term are having same variable , then we need to first do the mathematical operation and then put derivative sign, if they are in multiple variable, they we simply need to put derivative along with every term and then solve further.

Note: Here in the given question we need to express the rule of derivative which is used for sum, we write the general formulae used for the derivative for two variable, if here the variables, comes to be of “n” numbers then also the formulae will act same.