Calculus: the derivative: the power rule

Tutoring first-year calculus, finding derivatives is prominent. The tutor gives an example.

The following is by my understanding.

In yesterday’s post I mention finding relative extrema by solving for when the derivative is equal to zero. To begin with, how might one find the derivative?

The equation mentioned in yesterday’s post is y=2x^3 + 10x^2 – 11x -14. To find its derivative, one can use the sum rule, the constant multiple rule, the power rule, and the constant rule.

The sum rule says that one can take the derivative term by term. The constant multiple rule says to leave any constant multiplier in front of a term as you take the derivative, then multiply it back afterward. The power rule says that, for a variable to an exponent, bring its exponent to become a multiplier in front, then replace the exponent by itself minus one. The constant rule says that the derivative of a constant, not multiplied to a variable, is zero.

Therefore, the derivative of y=2x^3 + 10x^2 -11x -14 is 2(3x^2) + 10(2x^1) -11x^0 – 0 or just 6x^2 + 20x – 11.

Next post, I intend to continue with solving for when said derivative’s value is zero.

Source:

Larson, R.E., Hostetler, R.P. (1989). Calculus, part one, third edition. D.C. Heath and Company.