# Evaluate d/dr r(g(t)) using the chain rule: r(t) = g(t) = 6t-7

## Question:

Evaluate {eq}\displaystyle \frac{d}{dr} r(g(t)) {/eq} using the chain rule:

{eq}\displaystyle r(t) = \left \langle e^t, e^{9t}, 4 \right \rangle \ g(t) =6t-7 {/eq}

## Chain Rule:

Suppose an independent variable of a function is also a function of another variable. Then, the chain rule is used to differentiate the function. The differentiation method is the reverse process of the integration method.

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Given

• The function is {eq}r\left( t \right) = \left\langle {{e^t},{e^{9t}},4} \right\rangle {/eq} and {eq}g\left( t \right) = 6t - 7 {/eq}.

First...

Using the Chain Rule to Differentiate Complex Functions

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Chapter 8 / Lesson 6
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Learn how to differentiate complex functions using the chain rule. Review an explanation of the chain rule and how to use it to solve complex problems like functions without parentheses and trig functions.