Find the derivative of each of the following w.r.t $x$: $\mathrm{f}(x) = \ln (\tan x - \sin x)$

Question

Find the derivative of each of the following w.r.t $x$: $\mathrm{f}(x) = \ln (\tan x - \sin x)$ $y = \ln \sqrt{\cos^2 x \tan^3 x}$ $\mathrm{f}(x) = \ln (2x^4 - \cos 3x^5)$

Accepted Answer

(a) $\frac{\sec^2x-\cos x}{\tan x-\sin x}$ (b) $-\tan x+\frac32\frac{\sec^2x}{\tan x}$ (c) $\frac{8x^3+15x^4\sin(3x^5)}{2x^4-\cos(3x^5)}$

Logarithmic Functions with Trigonometry

Logarithmic Functions with Trigonometry

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