Find the 100th derivative of $x \sinh(2x)$ If $f(x) = x \sinh(2x)$, find $f^{({100})}(x)$.
My (Incorrect) working so far:
Using Leibniz' Formula for derivatives:
$$(fg)^{(n)}=\sum_{k=0}^n{n\choose k}f^{(k)}g^{(n-k)}$$
$$(x\sinh(2x))^{(100)}=\sum_{k=0}^{100}{100\choose k}f^{(k)}g^{(n-k)}=$$
Since the second derivative of $x$ is $0$...
$$=\sum_{k=0}^1{2\choose k}f^{(k)}g^{(n-k)}$$
$$={2\choose 0}(x)(\sinh(2x))+{2\choose 1}(1)(2\cosh(2x))$$
$$=4x \sinh(2x)+4 \cosh(2x)$$
This is my answer and it is not correct. What do I need to change to make it correct?
Thanks in advance.

The binomial coefficient in the Leibniz formula should be ${100\choose k}$ and not ${2\choose k}$.
