Question

Differentiate the function w.r.t.x:
$\rm \frac{x\tan x}{\sec x+\tan x}$

Answer 1

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Answer 2

Answer:

SecxTanx  + xSecxTan²x  + xSec³x   - Tan²x  - 2xTanxSec²x

Step-by-step explanation:

xtan(x)/ (secx + Tanx)

= (xtan(x)/ (secx + Tanx)  ) * (secx - Tanx)/(secx - Tanx)

= xtan(x) (secx - Tanx) /(sec²x - Tan²x)

= xtan(x) (secx - Tanx)     as sec²x - Tan²x = 1

= xtan(x)secx  - xtan²(x)

Let s=secx and t=tanx

⟹ds/dx=secx tanx=st

⟹dt/dx=sec²x=s²

f(x) = xst - xt²

f'(x) = st + xtds/dx + xsdt/dx  - t²  - 2xtdt/dx

f'(x) = st + xtst + xss²  - t²  - 2xts²

f'(x) = SecxTanx  + xSecxTan²x  + xSec³x   - Tan²x  - 2xTanxSec²x