Q. 1 TB - Calculus

Question

Chain rule: If $$f$$ is a function of $$x$$ and $$x$$ is a function of $$t$$, how is the chain rule used to find the rate of change of $$f$$ with respect to $$t$$?

Step-by-Step Solution

Answer

The rate of change of $$f$$ with respect to $$t$$ found using the Chain's rule is $$\frac{df}{dt}=\frac{df}{dx} \times \frac{dx}{dt}$$

Step 1. Given Information

$$f$$ is a function of $$x$$ and $$x$$ is a function of $$t$$ 

Step 2. Explanation

It is given that, $$f$$ is a function of $$x$$ and $$x$$ is a function of $$t$$ 

The rate of change of $$f$$ with respect to $$t$$ is $$\frac{df}{dt}$$

We can solve $$\frac{df}{dt}$$ using the Leibniz's notation of the Chain's rule.

Hence, using Chain's rule, we get the rate of change of $$f$$ with respect to $$t$$ as $$\frac{df}{dt}=\frac{df}{dx} \times \frac{dx}{dt}$$