Okay so first subtract 9x^2-10x+1 which gives you (9x -1)(x-1). then do the same to the next one which gives you -2(x^2 -2x +5) when you subtract you should get 11x^2 - 14x +11

6 0

2 years ago

How to solve derivative of (sin3x)/x using first principle

Leona [35]

$\dfrac{d}{dx}(\dfrac{\sin(3x)}{x})$

First we must apply the Quotient rule that states,

$(\dfrac{f}{g})'=\dfrac{f'g-g'f}{g^2}$

This means that our derivative becomes,

$\dfrac{\dfrac{d}{dx}(\sin(3x))x-\dfrac{d}{dx}(x)\sin(3x)}{x^2}$

Now we need to calculate $\dfrac{d}{dx}(\sin(3x))$ and $\dfrac{d}{dx}(x)$

$\dfrac{d}{dx}(\sin(3x))=\cos(3x)\cdot3$

$\dfrac{d}{dx}(x)=1$

From here the new equation looks like,

$\dfrac{3x\cos(3x)-\sin(3x)}{x^2}$

And that is the final result.

Hope this helps.

r3t40

7 0

2 years ago

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