Question

Select the correct answer from the given alternative:

Suppose f(x) is the derivative of g(x) and g(x) is the derivative of h(x).

If h(x) = a sin x + b cos x + c then f(x) + h(x) = 

Options

• 0

• c

• – c

• − 2(a sin + b cos x)

Answer 1

c

Explanation;

h(x) = a sin x + b cos x + c

Differentiate with respect to x,

h'(x) = a cos x – b sin x = g(x) …[given]

Differentiate with respect to x,

g'(x) = – a sin x – b cos x = f(x) …[given]

∴ f(x) + h(x) = – a sin x – b cos x + a sin x + b cos x + c

f(x) + h(x) = c