Question

If
y = cos^-1 [4cos^3 x - 3cosx] them [dy/dx] at x=2 is?​

Answer 1

Step-by-step explanation:

Given,

$y = \cos^{ - 1} (4 \cos(x) - 3 \cos(x) )$

$= > y = \cos^{ - 1} ( \cos(3x) )$

$= > y = 3x$

Differentiating both sides we get,

$\frac{dy}{dx} = 3$

so, dy/dx at x=2 is 3

Answer 2

The value of $\frac{dy}{dx}$  at x=2  is 3.

Step-by-step explanation:

Given:

$y=cos^{-1} [4cos^{3} x - 3 cosx]$

To Find:

The value of $\frac{d y}{d x}$  at x=2  

Formula Use:

$\frac{d y}{d x}$ denotes the differentiation of y with respect to the variable x.

$y= f(x) =x$

then $\frac{d (x)}{d x} =1$    --------------------------------------- formula no .01

$cos3x=4 xcos^{3} - 3 cosx$   --------------------  formula no.02

Solution:

As given-$y=cos^{-1} [4cos^{3} x - 3 cosx]$

Applying formula no. 02

$cos3x=4 xcos^{3} - 3 cosx$

$y=cos^{-1} [4cos^{3} x - 3 cosx]$

  $= cos^{-1} [ cos3x]$

  $= 3x$

$y=3x$

Differentiating both sides with respect to x, we get.

$\frac{dy}{dx} = \frac{d(3x)}{dx}$

    $= \frac{3 d(x)}{dx}$

Putting the value of $\frac{d (x)}{d x} =1$ form formula no. 02

$\frac{dy}{dx} =3( 1)$

$\frac{dy}{dx} =3$

At x=2 The value of $\frac{dy}{dx}$   = 3

Thus. the value of The value of $\frac{dy}{dx}$ at x=2  is 3.