please include steps. :)
f(x) = √(1 + 2tanx )
. . . . . (1 + 2tanx)'
f'(x)=▬▬▬▬▬▬▬
. . . . 2√(1 + 2tanx )
. . . . . 0 + 2(tanx)'
. . . . . . .2
. . . . .▬▬▬
. . . . . cos²x
. . . . . . . . . . . .2
f'(x) = ▬▬▬▬▬▬▬▬▬
. . . . . 2cos²x√(1 + 2tanx )
. . . . . . . . . . . .1
. . . . . cos²x√(1 + 2tanx )
Derivative f'(x) = 1/2(1+2tanx) ^ -1/2 *2sec^2x
f(x)= â(1+2tanx)
f'(x) = 1/2 (1+2tanx)^(-1/2) * d/dx (1+2tanx)
f'(x) = 1/2 (1+2tanx)^(-1/2) * 2sec^2(x)
f'(x) = sec^2(x) / â(1+2tanx)
given f(x) = y=[1+tanx]^1/2
let 1+tanx =u
y=u^1/2
dy/dx= dy/du *du/dx
dy/du = 1/2u^-1/2
u = 1+tanx
du/dx =0+sec^2x
dy/dx= dy/du*du/dx= 1/2u^-1/2*sec^2x
f'(x) =1/2[1+tanx]^-1/2 (sec^2x)
=sec^2x/2(1+tanx)^1/2
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Verified answer
f(x) = √(1 + 2tanx )
. . . . . (1 + 2tanx)'
f'(x)=▬▬▬▬▬▬▬
. . . . 2√(1 + 2tanx )
. . . . . 0 + 2(tanx)'
f'(x)=▬▬▬▬▬▬▬
. . . . 2√(1 + 2tanx )
. . . . . . .2
. . . . .▬▬▬
. . . . . cos²x
f'(x)=▬▬▬▬▬▬▬
. . . . 2√(1 + 2tanx )
. . . . . . . . . . . .2
f'(x) = ▬▬▬▬▬▬▬▬▬
. . . . . 2cos²x√(1 + 2tanx )
. . . . . . . . . . . .1
f'(x) = ▬▬▬▬▬▬▬▬▬
. . . . . cos²x√(1 + 2tanx )
Derivative f'(x) = 1/2(1+2tanx) ^ -1/2 *2sec^2x
f(x)= â(1+2tanx)
f'(x) = 1/2 (1+2tanx)^(-1/2) * d/dx (1+2tanx)
f'(x) = 1/2 (1+2tanx)^(-1/2) * 2sec^2(x)
f'(x) = sec^2(x) / â(1+2tanx)
given f(x) = y=[1+tanx]^1/2
let 1+tanx =u
y=u^1/2
dy/dx= dy/du *du/dx
dy/du = 1/2u^-1/2
u = 1+tanx
du/dx =0+sec^2x
dy/dx= dy/du*du/dx= 1/2u^-1/2*sec^2x
f'(x) =1/2[1+tanx]^-1/2 (sec^2x)
=sec^2x/2(1+tanx)^1/2