Question

if y=
log (tan 4-3x)
find dy/dx​

Answer 1

SOLUTION

GIVEN

y = log [ tan ( 4 - 3x )]

TO DETERMINE

$\displaystyle \sf{ \frac{dy}{dx} }$

EVALUATION

Here it is given that

y = log [ tan ( 4 - 3x )]

Now Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} = \frac{d}{dx} \log \tan(4 - 3x)}$

$\displaystyle \sf{ \implies \frac{dy}{dx} = \frac{1}{\tan(4 - 3x)} \frac{d}{dx} \tan(4 - 3x)}$

$\displaystyle \sf{ \implies \frac{dy}{dx} = \frac{1}{\tan(4 - 3x)} \times { \sec}^{2} (4 - 3x) \times \frac{d}{dx} (4 - 3x)}$

$\displaystyle \sf{ \implies \frac{dy}{dx} = \frac{1}{\tan(4 - 3x)} \times { \sec}^{2} (4 - 3x) \times - 3}$

$\displaystyle \sf{ \implies \frac{dy}{dx} = - 3 \times \frac{{ \sec}^{2} (4 - 3x)}{\tan(4 - 3x)} }$

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