The higher derivative of function product uses Leibniz formula (not Newton-Leibniz formula)

Remember that u (x) = x 2; v(x)= sin(x)； That is y(x)=u(x)*v(x)

Then use the following Leibniz formula:

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Obviously, the final result is only a few terms, because the derivative of u (x) = x 2 is 0 when calculating the third derivative. So the result must be three. Just put it carefully in the formula.

Finally, it is equal to: u * v (80th order)+80 * u' * v (79th order)+(80 * 79/2) * u'' * v (78th order).

=x^2*sin(x)+80 * 2x *(cos(x))+3 160 * 2 *(sin(x))= ......