Question

Find (dy)/(dx) if y=cot^(-1)(cot x)​

Answer 1

Step-by-step explanation:

The answer is

y

'

=

−

1

1

+

x

2

We start by using implicit differentiation:

y

=

cot

−

1

x

cot

y

=

x

−

csc

2

y

d

y

d

x

=

1

d

y

d

x

=

−

1

csc

2

y

d

y

d

x

=

−

1

1

+

cot

2

y

using trig identity:

1

+

cot

2

θ

=

csc

2

θ

d

y

d

x

=

−

1

1

+

x

2

using line 2:

cot

y

=

x

The trick for this derivative is to use an identity that allows you to substitute

x

back in for

y

because you don't want leave the derivative as an implicit function; substituting

x

back in will make the derivative an explicit function.

Answer link

Answer 2

Answer:

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