# 1. Assume that x and y are both differentiable functions of t. y = 2(x^{2} - 3x) a) Find dy/dt...

## Question:

1. Assume that {eq}x {/eq} and {eq}y {/eq} are both differentiable functions of {eq}t {/eq}.

$$y = 2(x^{2} - 3x)$$

a) Find {eq}\frac{dy}{dt} {/eq} when {eq}x = 5 {/eq}, given that {eq}\frac{dx}{dt}= 4 {/eq}.

b) Find {eq}\frac{dx}{dt} {/eq} when {eq}x = 7 {/eq}, given that {eq}\frac{dy}{dt} = 4 {/eq}.

2. The radius of a right circular is given by {eq}\sqrt{t + 6} {/eq} and its height is {eq}\frac{1}{6} \sqrt{t} {/eq}, where {eq}t {/eq} is time in seconds and the dimensions are in inches. Find the rate of change of the volume with respect to time.

## Differentiation:

Differentiation can be defined as differentiate all the variables in the equation with respect to the dependent variable. The differentiation in the equation also tells the higher order of the derivative. The differentiation is used to find the rate of change of the variable.

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Given data:

• {eq}y = 2\left( {{x^2} - 3x} \right) {/eq}
• {eq}\dfrac{{dx}}{{dt}} = 4 {/eq}
• {eq}x = 5 {/eq}

(1)

(a)

The given data is...