Question

Differentiate the following polynomial and algebraic expressions? `y = 7x^3 + 9x^2 - 12x + 60`

Answer 1

To differentiate a polynomial of this type, one uses the Power Rule on each term, except the constant term; the derivative of a constant is always 0.

Explanation:

The power rule is `f'(x^r) = rx^(r-1)`

Applying the power rule to each term of:

`y = 7x^3 + 9x^2 - 12x + 60`:

`f'(7x^3) = 21x^2`

`f'(9x^2)= 18x^1= 18x`

`f'(-12x)=-12x^0=-12`

Finally, the exception for f'(60) = 0#

Putting this all together:

`y' = 21x^2+18x-12`