Question

d / dx ( sin x / log x ) = ?​

Answer 1

Answer:

(1) (sin x)log x { [log(sin x)/x] + cot x}

(2) (sin x)log x { [log(sin x)/x] + cot x log x }

(3) (sin x)log x { [log(sin x)/x] + log x }

(4) none of these

Solution:

Let y = (sin x)log x

Take log on both sides

log y = log x log(sin x)

Use product rule and differentiate w.r.t.x

(1/y)dy/dx = (1/x) × log(sin x) + log x × (1/sin x) × cos x

= [log(sin x)/x] + cot x log x

dy/dx = y{ [log(sin x)/x] + cot x log x }

= (sin x)log x { [log(sin x)/x] + cot x log x

Explanation: