Question

The derivative of sin x with respect to log x is ____________.

Options

• cos x

• x cos x

• `"cos x"/"log x"`

• `1/"x"` cos x

Answer 1

The derivative of sin x with respect to log x is x cos x.

Explanation:

as y = sin x, t = log x `"dy"/"dx" = "dy"/"dx" div "dt"/"dx"`

`= "d"/"dx" ("sin x") div "d"/"dx" ("log x")`

`= "cos x" div 1/"x" = "x cos x"`