Homework SourseSuppose f and g are differentiable functions with the values
Suppose f and g are differentiable functions with the values shown in the following table.
x f(x) g(x) f\'(x) g\'(x)
-1, 2, 1, -1, 3
0, 1, 1, 2, 3
1, -1, -3, 2, -4
Find the value of h\'(1), where h(x) = f(x)g(x)
Find the value of k\'(0), where k(x) = f(x)/g(x)
Find the value of m\'(-1) where m(x) = f(g(x))
Please show work
x f(x) g(x) f\'(x) g\'(x)
-1, 2, 1, -1, 3
0, 1, 1, 2, 3
1, -1, -3, 2, -4
Find the value of h\'(1), where h(x) = f(x)g(x)
Find the value of k\'(0), where k(x) = f(x)/g(x)
Find the value of m\'(-1) where m(x) = f(g(x))
Please show work
Solution
h\'(1) = f\'(x)g(x) +f(x)g\'(x) = (-1)(-4) + (2)(-3)= -6 + 4 = -2 k\'(0) = g(x) f\'(x) -f(x) g\'(x) / g(x)*g(x) : 2 - 3 / 1 = -1 m\'(-1) = f\'(g(x)) * g\'(x) = 3*[ 2 ] = 6
