Question

Differentiate the following w.r.t.x:

y = (25)^log₅(secx) − (16)^log₄(tanx) 

Answer 1

y = (25)^log₅(secx) − (16)^log₄(tanx) 

y = (5²)^log₅(secx) − (4²)^log₄(tanx) 

y = (5)^{2log₅(secx)} − (4)^{2log₄(tanx)} 

`y = (5)^(log_5 (sec^2x)) - (4)^(log_4(tan^2x))`

y =  sec²x – tan²x                      ...`[ ∵ a^(log_ax) = x]`

∴ y = 1
Differentiating w.r.t.x, we get,

`"dy"/"dx" = "d"/"dx"(1)`

`"dy"/"dx"` = 0.