This would be my approach:
Let and
Then use the product rule:
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.
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?