given that f(x)=x^11h(x)
h(-1)=4
h'(-1)=7
find f'(-1)
f'(x)=11x^10*h(x)+x^11*h'(x)
f'(-1)=11(-1)^10*h(-1)+(-1)^11*h'(-1)
To find f'(-1), we need to differentiate the function f(x) = x^11 * h(x) with respect to x and then evaluate it at x = -1.
First, we can use the product rule of differentiation, which states that if we have two functions u(x) and v(x), then the derivative of their product is given by:
(d/dx)(u(x)*v(x)) = u'(x)*v(x) + u(x)*v'(x)
Applying this rule to f(x) = x^11 * h(x), we have:
f'(x) = (d/dx)(x^11 * h(x))
= 11x^10 * h(x) + x^11 * h'(x)
Now, let's evaluate this derivative at x = -1:
f'(-1) = 11*(-1)^10 * h(-1) + (-1)^11 * h'(-1)
= 11 * 1 * h(-1) - 1 * h'(-1)
= 11 * 1 * 4 - 1 * 7
= 44 - 7
= 37
Therefore, f'(-1) = 37.