Math, asked by zebaanzari360, 10 months ago

Differentiation of cos(x-y)

Answers

Answered by AllRoundedWarriors
0

Answer:

-sin (a)

Step-by-step explanation:

This is 'CHAIN RULE.'

To solve this question we need to know that to whose respect we are differentiating. But, here i am differentiating with respect to x. So,

let \: (x - y) = a

so now differentiate 'cos a' we get,

 \frac{d}{dx}  \cos(a)  =  -  \sin(a)

as we now that actually we are differentiating cos

(x-y) and not cos (a) so we will differentiate (x-y) using difference rule.

 \frac{d}{dx} (x - y) =  \frac{d}{dx} x -  \frac{d}{dx} y \\ 1 - 0 = 1

as differentiation of y will be 0 as we are differentiating with respect to x so Final Answer = 1 X - sin (a)

= - sin (a)

Answered by BrainlyYoda
0

Question:

Differentiation of cos(x-y)

Solution:

\frac{d}{dx} [cos(x-y)]\\

(- sin(x - y)) * \frac{d}{dx} [x-y]

- (\frac{d}{dx} [x] + \frac{d}{dx} [-y]) sin(x-y)

-(1 + 0)sin(x - y)

- sin(x - y)

The differentiation of cos(x-y)  is  [-sin(x - y)]

Explanation:

We have applied chain rule along with differentiation rule of

[cos(u(x))]' = - sin(u(x)) * u'(x)

The sign [ ' ] here means single time differentiation.

As there are more signs number of differentiation times increases.

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