Given that f(x)=(x^(11))(h(x)), h(-1)=5, h'(-1)=8. Calculate f'(-1).

You will need the power rule and product rule.

f '(x) = [(d/dx) x^11] * h(x) + x^11 * h'(x) by the product rule
.......= 11x^10 h(x) + x^11 h'(x).

Let x = -1:
f '(-1) = 11 * (-1)^10 * h(-1) + (-1)^11 * h'(-1)
........= 11 * 1 * 5 + (-1) * 8
........= 47.

I hope this helps!