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Find The Derivative Of x³ With These Two Methods

Find The Derivative Of x³ With These Two Methods


When being asked the derivative of x3, it is important to not overcomplicate it.

The derivative of x3 can be a very simple question if you have practice using the power rule which can be applied to polynomials of the form axˆn.

The derivative of axn using the formula is anxn-1

In this case where n=3 and a=1. 

The derivative of x3 is 3x2

Solving the derivative of x3 from first principles:

The first principles formula is dy/dx = [f(x+h)-f(x)]/h  as h approaches 0.

Let f(x)=x3, and f(x+h)=(x+h)3.

Next we need to expand the (x+h) bracket and we can use binomial expansion here.

(x+h)3 = x0h3 + 3x1h2 + 3x2h1 + x3h0

Which simplifies to h3 + 3xh2 + 3x2h + x3

Now we make the substitution into the formula.

[h3 + 3xh2 + 3x2h + x3 - x3]/h

We are left with [h2 + 3xh +3x2]

As h tends to 0, we are left with 3x2. This proves that 3x2 is the derivative of x3

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Author: MyEdSpace
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