Question

tan³x,Find the derivative of the given function defined on proper domains.

Answer 1

it is given that function, f(x) = tan³x
we have to find the derivative of the given function.

f(x) = tan³x

df(x)/dx = d{tan³x}/dx

we know, if y = gⁿ(x) then, $\frac{dy}{dx}=n.g^{n-1}(x).g'(x)$

so, f'(x) = d{tan³x}/dx = 3tan²x. d{tanx}/dx

= 3tan²x. sec²x

= (√3tanx. secx)²

hence, first order derivative of the given function is (√3tanx.secx)²

Answer 2

HELLO DEAR,

let f(x) = tan³x.

we know, if y = hⁿ(x) then, $\bold{\frac{dy}{dx}=n.h^{n-1}(x).h'(x)}$


so, f'(x) = tan³x/dx

=> f'(x) = 3tan²x.(tanx)/dx

=> f'(x) = 3tan²x.sec²x

=> f'(x) = {√3tanx.secx}²


I HOPE ITS HELP YOU DEAR,
THANKS