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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Given $y = x^2$, we need to find $\frac{dy}{dt}$

step 2

To find $\frac{dy}{dt}$, we use the chain rule: $\frac{dy}{dt} = \frac{dy}{dx} \cdot \frac{dx}{dt}$

step 3

First, we differentiate $y = x^2$ with respect to $x$: $\frac{dy}{dx} = 2x$

step 4

Now, we multiply by $\frac{dx}{dt}$: $\frac{dy}{dt} = 2x \cdot \frac{dx}{dt}$

Answer

$\frac{dy}{dt} = 2x \cdot \frac{dx}{dt}$

Key Concept

Chain Rule

Explanation

The chain rule is used to differentiate a function with respect to a variable that is itself a function of another variable.

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