Question

If y= log cosx then dy dx​

Answer 1

EXPLANATION.

⇒ y = ㏒(cos x).

As we know that,

Differentiate w.r.t x, we get.

⇒ dy/dx = d/dx ㏒(cos x).

⇒ dy/dx = 1/(cos x) x d(cos x)/dx.

⇒ dy/dx = 1/(cos x) x (- sin x).

⇒ dy/dx = (-sin x)/(cos x).

⇒ dy/dx = - tan x.

                                                                                                                   

MORE INFORMATION.

(1) = d(sin x)/dx = cos x.

(2) = d(cos x)/dx = - sin x.

(3) = d(tan x)/dx = sec²x.

(4) = d(cot x)/dx = - cosec²x.

(5) = d(sec x)/dx = sec x tan x.

(6) = d(cosec x)/dx = - cosec x cot x.

Answer 2

Step-by-step explanation:

Differentiating w.r.to x,

dy/dx=d/dx(logcosx)

dy/dx=(1/cosx)d/dx(cosx)

dy/dx=(1/cosx)-sinx

dy/dx= -tanx