Question

If y = cot x, dy/dx is

(-cosec2x)
sin2x
(cosec2x)
cot x cosec x​

Answer 1

SOLUTION

GIVEN

y = cot x

TO CHOOSE THE CORRECT OPTION

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

• - cosec²x

• sin 2x

• cosec²x

• cot x cosec x

EVALUATION

Here it is given that

y = cot x

Differentiating both sides with respect to x we get

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

$\displaystyle \sf{ =\frac{d}{dx} ( \cot x ) }$

= - cosec²x

FINAL ANSWER

Hence the correct option is

- cosec²x

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Answer 2

Given :  y = cot x

To Find : dy/dx

(-cosec²x)

sin²x

(cosec²x)

cot x cosec x​

Solution:

y   = cotx

cotx = cosx/sinx

=> y  = cosx/sinx

dy/dx =  (d/dx)(cosx/sinx)

Applying chain rule

(d/dx)cosx/ sinx   + cosx(d/dx)(1/sinx)

= -sinx / sinx  + cosx (-1/sin²x) cosx

=  - 1  - cos²x/sin²x

= -(1 + cos²x/sin²x)

= - (  (sin²x + cos²x)/sin²x )

= - ( 1/ sin²x )

=  - cosec²x

dy/dx =  =  - cosec²x

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