Question

If y = 3x3 + 4x and dx dt = 3, find dy dt when x = 2.

Answer 1

$y = 3x^3 + 4x\ \Rightarrow\displaystyle\ \frac{dy}{dt} = 9x^2 \frac{dx}{dt} + 4\frac{dx}{dt} \Rightarrow \\ \\ \frac{dy}{dt} = 9(2)^2 (3) + 4(3) = 120$

Answer 2

The differentiation of y with respect to t, dy/dt = 120

To answer the question, we need to differentiate the function

How to differentiate the function

Since

• y = 3x³ + 4x and
• dx/dt = 3.

We need to find dy/dt when x = 2

Derivative dy/dt

Differentiating y with respect to t, we have

dy/dt = d(3x³ + 4x )/dt

= d(3x³)/dt + d4x/dt

= d(3x³)/dx × dx/dt + d4x/dx × dx/dt

= 9x²dx/dt + 4dx/dt

Given that dx/dt = 3, substituting this into the equation, we have

dy/dt = 9x²dx/dt + 4dx/dt

dy/dt = 9x² × 3 + 4 × 3

dy/dt = 27x² + 12

When x = 2, we substitute x into the equation, we have

dy/dt = 27x² + 12

dy/dt = 27(2)² + 12

dy/dt = 27 × 4 + 12

dy/dt = 108 + 12

dy/dt = 120

So, the differentiation of y with respect to t, dy/dt = 120

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