evaluate the function

Question

given that f(x)= (x^6)h(x)

 

h(-1)= 4

h'(-1) = 7

 

f'(x)= ???

Answer 1

f(x) = x⁶h(x)

 

By the product rule, f'(x) = 6x⁵h(x) + x⁶h'(x)

 

So, f'(-1) = 6(-1)⁵h(-1) + (-1)⁶h'(-1)

 

                = 6(-1)(4) + (1)(7) = -24 + 7 = -17