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Differential Calculus> y=cos^-1(8x^4-8x^2+1), prove that dy/dx=-...

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y=cos^-1(8x^4-8x^2+1), prove that dy/dx=-4/(1-x^2)^1/2

Mostafijur Rahaman , 11 Years ago

Grade 12

1 Answers

Arun Kumar

Last Activity: 11 Years ago

$\frac{\mathrm{dcos^{-1}x} }{\mathrm{d} x}=-1/\sqrt{1-x^2} \\\frac{\mathrm{d} y}{\mathrm{d} x}=-16(2x^3-x)/(\sqrt{1-(8x^4-8x^2+1)^2}) \\=-16(2x^3-x)/((-8x^4+8x^2)(8x^4-8x^2+2)) \\=-16(2x^3-x)/\sqrt{(16x^2(1-x^2)(2x-1)^2)} \\=-16x(2x^2-1)/\sqrt{(16x^2(1-x^2)(2x^2-1)^2)}$

which on little solving gives the answer

Arun Kumar

IIT Delhi

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