# Find the derivative of x+cosx÷tanx with respect to x?

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Feb 25, 2017

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# d/dx (x+cosx ÷ tanx ) = 1 - cosx - cotxcscx #

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# d/dx (x+cosx ÷ tanx ) = d/dx (x+cosx/tanx ) #

# " "= d/dx (x)+d/dx(cosx/tanx) #

# " "= 1 + { (tanx)(-sinx) - (cosx)(sec^2x) }/ (tanx)^2 #

# " "= 1 - (tanx)(sinx)/tan^2x - (cosx)(sec^2x)/(tanx)^2 #

# " "= 1 - (sinx)*cosx/sinx - (cosx)(1/cos^2x)*cos^2x/sin^2x #

# " "= 1 - cosx - (cosx)/sin^2x #

# " "= 1 - cosx - cotxcscx #

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