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

1 Answer
Mar 25, 2018

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#