Derivative of x 3 is defined as the differentiation of x^3. This differentiation is guided by the following general formula:-
Formula is d(x^n)/ dx = n x^ (n-1)
Here x is the variable involved whose differentiation is to be calculated and n is its exponent/power.
This tool helps in finding the differentiation of the terms involving x^3. The terms can be interconnected by the addition, multiplication, subtraction, or division operator. This tool uses step by step procedure along with formulas to evaluate the solution of problem involving x^3.
This can be more clarified by the following suitable examples.
Question 1: Find out the derivative by using addition rule of function y = 10 + x^3 with respect to x.
Solution: Given y = 10 + x^3
So by using addition rule of differentiation,
We get dy/dx = d (10)/dx + d(x^3)/dx
= 0 + d(x^3)/dx (because differentiation of constant function is zero)
= 0 + 3 x^ (3-1) (because we know that d(x^n)/ dx = n x^ (n-1))
So dy/dx = d (10 + x^3)/dx = 3x^2 is the required answer.
Question 2: Find out the differentiation of y = 1000 (x^3)
Solution: Given y = 1000 (x^3)
We know that, d (kx)/dx = k. dx/dx
Therefore dy/dx = d (1000 (x^3))/ dx = 1000 d(x^3)/dx
= 1000 (3 (x) ^ (3-1))
= 1000 (3x^2)
= 3000 x^2
Hence dy/dx = d (1000 (x^3))/ dx = 3000 x^2 is the required differentiation of function y.