Bradford T. answered 12/17/20
Retired Engineer / Upper level math instructor
Let k(x) = 3x, k '(x) = 3
h(x) = g(f(k(x)))
h '(x) = g'(f(k(x))•f '(k(x))•k'(x)
h'(1) = g'(f(3))•f '(3)•k'(1)
= g'(2)•10•3
= 5•10•3 = 150
Jon B.
asked 12/17/20Use the table below to evaluate the derivative with respect to x of g of f of 3 times x at x = 1.
x 1 2 3 4
f(x) 6 1 2 2
f ′(x) 6 1 10 2
g(x) 1 4 4 3
g ′(x)4 5 7 –4
Bradford T. answered 12/17/20
Retired Engineer / Upper level math instructor
Let k(x) = 3x, k '(x) = 3
h(x) = g(f(k(x)))
h '(x) = g'(f(k(x))•f '(k(x))•k'(x)
h'(1) = g'(f(3))•f '(3)•k'(1)
= g'(2)•10•3
= 5•10•3 = 150
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