Question

Let f and g be differentiable function such that f¢(x) = 2g(x) and g¢(x) = –f(x), and let T(x) = (f(x))² – (g (x))².

Then T¢(x) is equal to

• A. T(x)
• B. 0
• C. 2f(x) g(x)
• D. 6f(x) g(x)

Answer 1

Answer: (D)

6f(x) g(x)

Answer 2

T¢(x) = 2(f(x) f¢(x) – g(x) g¢(x))

= 2(2g(x) f(x) + f(x) g(x))

= 6f(x) g(x)