I am asked to derive AND simplify this:
$$\sin(10^{7x^2+2x}\cdot 10^{7x+3})$$
First, I join the powers together and get:
$$\sin(10^{7x^2+9x+3})$$
Then, once derived, I get this:
$$\cos(10^{7x^2+9x+3}) \cdot 10^{7x^2+9x+3}\cdot \ln(10)\cdot (14x+9)$$
I think it's correct (not absolutely sure though) But the "simplify" part of the question is bugging me. What do you think could be simplified here? Do you think this answer could be taken a step further?
Although I end up with a bunch of terms and multiplications, I don't see what I could blend together in order to make it more simplified than it is.
Thank you.
PS: if you want to see the derivation intermediate steps, just ask. It's just that it's too long to format and that it doesn't seem relevant to my question (unless I made a mistake somewhere).
Your derivative is correct, and cannot further be simplified.