The power rule

Calculus Tutorial

The power rule

Intro

The power rule is used to take derivatives of a variable raised to a power. When asked to take the derivative of say, x^2 (x squared), you bring the exponent down and multiply it by the existing coefficient, to become a coefficient of the variable, now you look back up at the exponent and subtract one. This leaves you with 2x^1, “two x to the first power”, or simply 2x. since you don’t need to state something raised to the first power.

Sample Problem

find the derivative;
y=3x^4

y’=12x^4


y’=7x^4


y’=12x^3


y’=7x^3


y’=12x^3


Solution

y=3x^4;
bring down the exponent and multiply by the existing coefficient;
12x^4;
now subtract one from the exponent;
y’=12x^3

the answer is y’=12x^3



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