# Thread: How do I differentiate y=(4x^2 - e^2x)sin3x ?

1. ## How do I differentiate y=(4x^2 - e^2x)sin3x ?

Hi, I have a seemingly straight forward question but I seem to get lost half way through! how do I differentiate y=(4x^2 - e^2x)sin3x ?

So far, I think: let y = z.sin3x where z = 4x^2 - e^2x

then dy/dz = 3x.z.cos3x and dz/dx = 8x - 2e^2x

I know I have to then apply the chain rule but that's where I go wrong, can anyone help please? Apologies for the format.

2. ## Re: How do I differentiate y=(4x^2 - e^2x)sin3x ?

$\displaystyle y=(4x^2 - e^{2x})sin3x$

This would be my approach:

Let $\displaystyle u=4x^2 - e^{2x}$ and $\displaystyle v=sin3x$

$\displaystyle \frac{du}{dx}=?$

$\displaystyle \frac{dv}{dx}=?$

Then use the product rule:

$\displaystyle \frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$

3. ## Re: How do I differentiate y=(4x^2 - e^2x)sin3x ?

Thanks, so du/dx = 8x - (2e^2x)

and dv/dx = 3cos3x

therefore, dy/dx = (4x^2 - e^2x)(3cos3x) + (sin3x)(8x - 2e^2x)

= (12x^2 - 3e^2x)(cos3x) + (8x - 2e^2x)(sin3x)

I'm not sure how to simplify this further, can someone help?

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