Example Problem. Chain Rule for Derivatives

p {margin: 0; padding: 0;} .ft00{font-size:19px;font-family:CourierNew;color:#000000;} .ft01{font-size:16px;font-family:CourierNew;color:#000000;} .ft02{font-size:16px;line-height:21px;font-family:CourierNew;color:#000000;} Chain Rule for Derivatives. Example Problem We can take the derivative of 3x squared minus 5 all raised to thefourth power by applying the chain rule. The clue here that we'regoing to use the chain rule is the fact that this is not a nicepolynomial function, it's not the product of two functions, it'snot the quotient of two functions. Instead, what we have is wehave something that is in parentheses is being raised to anexponent. Basically, we have a composite function. This looks likeu to the fourth power. So that means this is a part u, which is 3xsquared minus 5." The derivative of that is 6x. When you have a comparative function, it is often easier to usethe chain rule. In this example, you can use the chain rule tofind the derivative of u to the fourth power. The derivative of uis equal to four times x cubed, minus five cubed times x squared.There is no need to multiply out this expression because wealready know how to simplify exponents with the distributiveproperty.