When do i use product rule

Jim H. Determining the appropriate differentiation rule is related to the order of operations. Explanation: Look at the expression and ask yourself, "If I plugged in a number for the variable, what is the last operation I would do?

Related questions What is the Chain Rule for derivatives? See all questions in Chain Rule. Impact of this question views around the world. You can reuse this answer Creative Commons License. As we add more functions to our repertoire and as the functions become more complicated the product rule will become more useful and in many cases required.

We should however get the same result here as we did then. However, before doing that we should convert the radical to a fractional exponent as always. So, we take the derivative of the first function times the second then add on to that the first function times the derivative of the second function. This is NOT what we got in the previous section for this derivative. However, with some simplification we can arrive at the same answer.

This is what we got for an answer in the previous section so that is a good check of the product rule. In this case, unlike the product rule examples, a couple of these functions will require the quotient rule in order to get the derivative.

Here is the work for this function. Again, not much to do here other than use the quotient rule. It seems strange to have this one here rather than being the first part of this example given that it definitely appears to be easier than any of the previous two. In fact, it is easier. There is a point to doing it here rather than first. In this case there are two ways to do compute this derivative. There is an easy way and a hard way and in this case the hard way is the quotient rule.

This is an example of a what is properly called a 'composite' function; basically a 'function of a function'. The two functions in this example are as follows: function one takes x and multiplies it by 3; function two takes the sine of the answer given by function one.

We have to use the chain rule to differentiate these types of functions. This is because we have two separate functions multiplied together: 'x' takes x and does nothing a nice simple function ; 'cos x ' takes the cosine of x.

But note they're separate functions: one doesn't rely on the answer to the other! When do I use the chain rule and when do I use the product rule in differentiation?