How to show d/dx(tanx)^3=3 (tanx)^4+3(secx)^2-3?

1 Answer
Feb 26, 2018

Please refer to a Proof in the Explanation.

Explanation:

By the Chain Rule,

d/dx(tanx)^3=3(tanx)^2*d/dx(tanx),

=3(tanx)^2(sec^2x),

=3(tanx)^2{(tanx)^2+1},

=3(tanx)^4+3(tanx)^2,

=3(tanx)^4+3{(secx)^2-1},

=3(tanx)^4+3(tanx)^2-3, as desired!