Question

Given k(x)=6f(x)(h(x)−1), find k′(5).

A. k′(5)=0
B. k′(5)=6f′(5)(h(5)−1)
C. k′(5)=6f(5)h′(5)
D. k′(5)=6f′(5)(h(5)−1)+6f(5)h′(5)

Answer 1

To find k'(5), differentiate the function k(x) using the product rule and chain rule, and substitute x=5 to get k'(5) = 6f'(5)(h(5)-1) + 6f(5)h'(5).

Step-by-step explanation:

To find k'(5), we need to differentiate the function k(x) with respect to x and evaluate it at x = 5.

Given that k(x) = 6f(x)(h(x)-1), we can use the product rule and chain rule to find k'(x).

K'(x) = 6f'(x)(h(x)-1) + 6f(x)h'(x)

Substituting x = 5 into the above equation, we get k'(5) = 6f'(5)(h(5)-1) + 6f(5)h'(5).

Therefore, the correct answer is Option D. k'(5) = 6f'(5)(h(5)-1) + 6f(5)h'(5).