Question

y=a^1/2 loga cos x.Find dy/dx​

Answer 1

Answer:

Step-by-step explanation:

I Hope You Understand :-)

Answer 2

Answer:

Required value of $\frac{dy}{dx}$

is $- \sqrt{a} sinx$

Step-by-step explanation:

Get,

$y = \sqrt{a} log(a \cos(x) )$

This is a problem of Calculas.

We are differentiating y with respect to x,

$\frac{dy}{dx} = \frac{d}{dx} ( \sqrt{a} log(a \cos(x) ) = \sqrt{a} \frac{d}{dx} ( log(a \cos(x) ) = \sqrt{a} \times \frac{1}{a \cos(x) } \times \frac{d}{dx} (a \cos(x) ) = \frac{1}{a \cos( x) } \times \sqrt{a} ( - asinx) = - \sqrt{a} \frac{ \sin(x) }{ \cos(x) } = - \sqrt{a} tanx$

Required value of $\frac{dy}{dx}$is ($- \sqrt{a} tanx$)

Here applied formulas are

$1.\frac{d}{dx} ( log(x) ) = \frac{1}{x} \\ 2. \frac{d}{dx} (cosx) = - sinx$

Some extra formulas of calculas,

$1. \frac{d}{dx} ( \sin(x) ) = \cos(x ) \\ 2. \frac{d}{dx} ( \cos(x) ) = - \sin(x) \\ 3. \frac{d}{dx} ( \tan(x) ) = {sec}^{2} x \\ 4. \frac{d}{dx} ( \cot(x) ) = - {cosec}^{2} x \\ 5. \frac{d}{dx} ( \sec(x) ) = \sec(x) \tan(x) \\ 6. \frac{d}{dx} (cosec(x)) = - cosecxcotx$