Question

Find the derivative of a power function using the power rule

Answer 1

Let’s make up a random function, say:

f(x) = x^6

Now by power laws we can break this up into two parts:
f(x) = (x^2)*(x^4)

Since we are now multiplying two functions we can apply the product rule:

f’(x) = (2x)(x^4) + (x^2)(4x^3)

Now we can simplify since we are only dealing with x’s:

f’(x) = 2x^5 + 4x^5
f’(x) = 6x^5

If we do the power rule of our initial function, you will find that the two are equal.

Hope this helps!!