Question

d/dx{x^tanx} = value of this


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Answer 1

Answer:

y=lntanx

⇒dxdy=tanx1×21tanxsec2x

=21tanxsec2x=2sinxcosx1=csc2x

At x=4π

dxdy=1

Answer 2

Question :

d(x^tanx) / dx

Answer:

Let's have

y = x ^ tanx

log y = tan x × log x

1 / y × dy/dx = tanx × 1/x + sec^2 × logx

{ since,

》 logy = 1/y

》 d(tanx)/dy = sec^2

》 formula of UV = u × d/dx (v) + d/dy (u) + v

since , u = tanx and v = logy }

1/y × dy/dx = tanx / x + sec^2 × log x

dy/dx = y × [tanx / x + logx sec^x ]

dy/dx = x^tanx [ tanx /x + logx sec^x ]

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