Question

if y=2tanx-7secx then find dy/dx​

Answer 1

Answer:

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dy/dx = 2.sec²x - 7.tanx.secx

Step-by-step explanation:

y=2.tanx-7.secx

Differentiate the following equation -

∴ dy/dx = dy/dx [2.tanx-7.secx]

dy/dx = dy/dx (2.tanx) - dy/dx (7.secx)

         = 2.dy/dx (tanx) - 7.dy/dx (secx)

         = 2.$I_{1}$   -   7.$I_{2}$           --------------------------------------- 1)

Solve $I_{1}$ and  $I_{2}$

$I_{1}$ = dy/dx (tanx) = dy/dx (sinx/cosx)

   = [(cosx.cosx)-(sinx).(-sinx)]/cos²x    -------------(using quotient rule)

   = [cos²x+sin²x]/cos²x

   = 1/cos²x                                   -------------(using the cos²x+sin²x=1)

   = sec²x

$I_{2}$ = dy/dx (secx)        

   = dy/dx (1/cosx)      

   = [(cosx*0)-1.(-sinx)]/cos²x       ------------------ (using product rule)

   = (sinx)/cos²x

   = sinx/cosx.1/cosx

   = tanx.secx

put the value of $I_{1}$ and  $I_{2}$

Equation 1) becomes

dy/dx = 2.$I_{1}$ - 7.$I_{2}$

          = 2.sec²x - 7.tanx.secx