Assume that x and y are both differentiable functions of t a) Find dx/dt given x = 25 and...

Question:

Assume that {eq}x \enspace and \enspace y {/eq} are both differentiable functions of {eq}t {/eq}

{eq}y = \sqrt x {/eq}

a) Find {eq}\frac{\mathrm{d} x}{\mathrm{d} t} {/eq}, given {eq}x = 25 \enspace and \enspace \frac{\mathrm{d} y}{\mathrm{d} t} = 3 {/eq}

b) Find {eq}\frac{\mathrm{d} y}{\mathrm{d} t} {/eq}, given {eq}x = 9 \enspace and \enspace \frac{\mathrm{d} x}{\mathrm{d} t} =9 {/eq}

Differentiation:

Differentiation is the process of finding derivative.

Derivative is the rate of change of one quantity with respect to other.

Here, we will differentiate given function w.r.t t and will plug the given values to get required value.

Answer and Explanation: 1

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Given equation is

{eq}\displaystyle y = \sqrt x {/eq}

Let's differentiate w.r.t t

{eq}\displaystyle...

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Derivatives: The Formal Definition

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Chapter 7 / Lesson 5
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The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.


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