Could you please explain it so that I can find nth derivatives for other terms such as $\sin^3(x)$, $x^2e^{5x}$. Or also $x^2\sin(5x)$? Thanks in advance. I understand Leibniz's theorem but I am not being able to find the nth derivative for non standard functions. If there are any sites that you could refer to me or any excerpt from any textbook or sites that'd be great.
[Math] How to find the nth derivative for $\cos^3(x)$
calculusderivativestrigonometry
Best Answer
$$\cos^3 x = \frac 14 \big( 3 \cos x + \cos (3x) \big)$$
Now, writing down the $n$th derivative of the right-hand expression should be straight forward.
Similarly for $\sin^3 x$.
For 'mixed' functions such as $x^2\sin(5x)$ I don't know of any way to avoid the messiness of Leibniz rule.