UPSC NDA Math Model Paper 6

Consider, y=tan3θ=f(θ)
x=sec2θ=f(θ)
To find

dy

dx

, use chain rule

dy

dx

=

dy dθ

dx dθ

........(1)
Here, y=tan3θ

dy

dθ

=3tan2θsec2θ
Now, x=sec2θ

dx

dθ

=2sec2θ‌tan‌θ
Put these values in equation (1), we get

dy

dx

=

3

2

‌tan‌θ
To find

dy

dx

at θ=

π

3

Put θ=

π

3

in above equation.

dy

dx

=

3√3

2

Hence, Derivative of tan3θ w.r.t. to sec2θ=

π

3

is

dy

dx

=

3√3

2