Question

For the curve y=(2x+1)³ find the rate of change of slope of the tangent

Answer 1

please give me brillant marks

Answer 2

$\dfrac{dy}{dx} = 24x^2 + 24x + 6$

is the rate of change of slope.

Step-by-step explanation:

We are given the following in the question:

$y = (2x+1)^3$

We have to find the rate of change of slope.

The rate of change of slope will be given by:

$\displaystyle\frac{dy}{dx} = \frac{d}{dx}(2x+1)^3\\\\\frac{dy}{dx} = 3(2x+1)^2(2)\\\frac{dy}{dx} = 6(4x^2 + 1 +4x)\\\frac{dy}{dx} = 24x^2 + 24x + 6$

Thus, the rate of change of slope is

$\dfrac{dy}{dx} = 24x^2 + 24x + 6$

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