Theorems+on+Differentiation+(power,+chain,+etc.)

__Power Rule__ To use the power rule, one must first evaluate the function. If an exponent is raised to a power, then this rule is applicable. The power rule allows one to take the derivative of a function faster than if they were to use the definition of the derivative. To perform the power rule, simply take the exponent of the variable and multiply it by the constant in front of that variable. After this has been done, subtract one away from the original exponent.

Ex: f(x)=7x^2 f'(x)=14x

__Quotient Rule__ To use this rule, one can remember this simple little saying: LoDiHI-HiDiLo over LoLo. Di equates to taking the derivative. If it says DiHi, then that means one will be taking the derivative (Di) of the numerator (Hi) and so on.

Ex: f(x)=x/x^2 f'(x)=[(x^2)(1)-(x)(2x)]/(x^2)^2

__Chain Rule__ This rule is to be used with functions inside of functions. The rule here is that one must take derivative of the outer function times the inner function all multiplied by the derivative of the inner function.

Ex: f(g(x)) f'(g(x)) X g'(x)