Find the derivatives of the function with respect to corresponding ind – InterviewSolution

InterviewSolution

1.

Find the derivatives of the function with respect to corresponding independent variables.(i) y = sin x + cos x(ii) f(x) = x sin x

Answer»

(i) dy/dx = cos x + (-sin x) = cos x – sin x

(ii) f(x) = x sin x

f(x) = uv

⇒ f'(x) = uv’ + vu’ = u(du/dx) + v(dv/dx)

Now u = x ⇒ u’ = 1

v = sin x ⇒ v’ cos x

f'(x) = x (cos x) + sin x(1)

= x cos x + sin x

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