Question

differenciate 1\4tan^4x

Answer 1

Answer:

Explanation:

The overriding issue is the fourth power. You can deal with it through the chain rule:

d

d

x

[

u

4

]

=

4

u

3

⋅

u

'

Here, we have  

u

=

tan

(

x

)

, so

d

d

x

[

tan

4

(

x

)

]

=

4

tan

3

(

x

)

⋅

d

d

x

[

tan

(

x

)

]

Know that  

d

d

x

[

tan

(

x

)

]

=

sec

2

(

x

)

, hence

d

d

x

[

tan

4

(

x

)

]

=

4

tan

3

(

x

)

sec

2

(

x

)