1.

Select the appropriate option from the given alternatives.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) = (A) 0 (B) c (C) -c (D) -2(a sin x + b cos x)

Answer»

Correct option is:(B) c

h(x) = a sin x + b cos x + c 

Differentiating w.r.t. x, we get 

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

Differentiating w.r.t. x, we get 

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


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