# Find the first derivative of the function below. {eq}B = 3Q^3 (2Q - 3Q^2) {/eq}

## Question:

Find the first derivative of the function below.

{eq}B = 3Q^3 (2Q - 3Q^2) {/eq}

## Derivative:

Let {eq}y = f\left( x \right) {/eq} be a function and {eq}\delta y {/eq} is the change in {eq}y {/eq} corresponding to the change in independent variable {eq}\delta x {/eq} in {eq}x {/eq}. So, the average rate of change of the function is given by {eq}\dfrac{{\delta y}}{{\delta x}} = \dfrac{{f\left( {x + \delta x} \right) - f\left( x \right)}}{{\delta x}} {/eq} and this rate become instantaneous as {eq}\delta x \to 0 {/eq}. If this limit exists then it gives the derivative of the function.

## Answer and Explanation: 1

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Given

• A function {eq}B = 3{Q^3}\left( {2Q - {Q^2}} \right) {/eq}.

Simplifying the function as

{eq}B = 6{Q^4} - 9{Q^5} {/eq}

Differentiate the...

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