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Problem Let h ( x ) = arctan ( arcsin x 1 − x 2 ) h(x)=\arctan\!\left(\dfrac{\arcsin x}{\sqrt{1-x^{2}}}\right) h ( x ) = arctan ( 1 − x 2 arcsin x ) h ′ ( x ) h'(x) h ′ ( x ) 1 + x arcsin x 1 − x 2 1 − x 2 [ 1 + ( arcsin x ) 2 1 − x 2 ] \displaystyle \frac{1+\dfrac{x\arcsin x}{\sqrt{1-x^{2}}}}{1-x^{2}}\left[\,1+\dfrac{(\arcsin x)^{2}}{1-x^{2}}\right] 1 − x 2 1 + 1 − x 2 x arcsin x [ 1 + 1 − x 2 ( arcsin x ) 2 ] 1 + x arcsin x 1 − x 2 1 − x 2 \displaystyle \frac{1+\dfrac{x\arcsin x}{\sqrt{1-x^{2}}}}{1-x^{2}} 1 − x 2 1 + 1 − x 2 x arcsin x 1 + x arcsin x 1 − x 2 ( 1 − x 2 ) [ 1 + ( arcsin x ) 2 1 − x 2 ] \displaystyle \frac{1+\dfrac{x\arcsin x}{\sqrt{1-x^{2}}}}{(1-x^{2})\left[\,1+\dfrac{(\arcsin x)^{2}}{1-x^{2}}\right]} ( 1 − x 2 ) [ 1 + 1 − x 2 ( arcsin x ) 2 ] 1 + 1 − x 2 x arcsin x 1 − x arcsin x 1 − x 2 ( 1 − x 2 ) [ 1 + ( arcsin x ) 2 1 − x 2 ] \displaystyle \frac{1-\dfrac{x\arcsin x}{\sqrt{1-x^{2}}}}{(1-x^{2})\left[\,1+\dfrac{(\arcsin x)^{2}}{1-x^{2}}\right]} ( 1 − x 2 ) [ 1 + 1 − x 2 ( arcsin x ) 2 ] 1 − 1 − x 2 x arcsin x Browse the problem library