Power/Product/Quotient Rules of Derivatives

definition of the derivative

measures the rate at which the function's value changes as its input changes. It is defined as the limit of the average rate of change of the function over an interval as the interval shrinks to zero.

power rule

negative exponent rules

negative exponents for power rule

keep other values in the numerator/denominator, only moves the x’s and exponents

starting as fractions negative exponent power rule

fraction exponent power rule: bring the exponent down to multiply it by the coefficient, and subtract 1 from the exponent

make sure to move all negative exponents in the end solution to the denominator

breaking fractional exponents down into roots: the numerator becomes the value under the root and the denominator becomes the root

root derivative example

derivative product rule for two functions

product rule for three+ functions

quotient rule

***the numerator may be a constant, still apply product rule with a

quotient rule example