# How do I find the derivative of #y=3x(6x-5x^2)#?

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To find the derivative of ( y = 3x(6x - 5x^2) ), you can use the product rule of differentiation.

Apply the product rule, which states that if ( y = uv ), where ( u ) and ( v ) are functions of ( x ), then the derivative ( \frac{dy}{dx} ) is given by ( \frac{dy}{dx} = u'v + uv' ), where ( u' ) and ( v' ) are the derivatives of ( u ) and ( v ) with respect to ( x ) respectively.

In this case, let ( u = 3x ) and ( v = (6x - 5x^2) ). Then,

[ u' = 3 ] [ v' = 6 - 10x ]

Apply the product rule:

[ \frac{dy}{dx} = (3)(6x - 5x^2) + (3x)(6 - 10x) ]

[ = 18x - 15x^2 + 18x - 30x^2 ]

[ = 36x - 45x^2 ]

So, the derivative of ( y = 3x(6x - 5x^2) ) is ( \frac{dy}{dx} = 36x - 45x^2 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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