ME-C2 Differentiating inverse trig functions
Finding the derivativesfor inverse trigonometric functionsThis resource has been developed to support teachers understand the technique of for differentiating inverse trigonometric functions.Find ddx(sin-1x)?Let y=sin-1x∴siny=xThink of siny=x1 and represent this as a right-angled triangle, shown below.Find the missing side by using Pythagoras’ theorem and interpret results for cosy and tany.cosy = 1-x2 and tany =x1-x2From ∴siny=x,dxdy=cosyand using the result cosy = 1-x2 givesdxdy=1-x2∴dydx=11-x2Therefore ddx(sin-1x)=11-x2?Using a similar technique to the one outlined above show thatddx(cos-1 x)=-11-x2and ddx(tan-1 x)=11+x2 ................
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