In such case, you won’t get away with chain rule alone. For example, imagine a function which itself is a product of two composite functions. Also be ready to use several rules simultaneously, if your particular homework implies this. However, note that in contrast to this example, chain rule is sometimes the only option, so be attentive. Needless to say, without chain rule you’d be still calculating the coefficients in binomial formula. So, firstly we need to determine what function is inside and what is outside. Substitute all the derivatives into the formula for chain rule. This time the argument is simply “ x” (or some other symbol due to initial denotation).ĥ. Proceed if there’s more than one outside function.Ĥ. Find derivative of the outside function due to table of derivatives using the whole enclosed expression as an argument.ģ. Let’s follow the chain rule algorithm we described before. So let’s try to use chain rule instead, you’ll appreciate simplification it suggests. But not that fast, we have 10th power and opening the braces would be a troublesome business. In fact, in this particular case, we can just open the braces using binomial theorem and obtain a polynomial, derivative of which is easily found due to table of derivatives. Suppose we need to find the first derivative of the following function: In this section we’re going to show you an example of using chain rule. If your function is not among common ones, you need to apply special rules to find its derivative: product rule, quotient rule, chain rule, etc. Taking a calculus class, you’ll surely be asked to find derivatives of functions.
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