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MathsHardMCQ2013 · 09 Apr Online

Q84.If x = ∫y0 √1+t2dt , then dx2d2y (1) y (2) √1 + y2 (3) x (4) y2 √1+y2

What This Question Tests

This question is a multi-step problem that requires differentiating an integral, finding the first derivative of an inverse function, and then applying the chain rule to find the second derivative.

Concepts Tested

Leibniz rule for differentiation of integralsDerivative of inverse functionChain rule for differentiation

Formulas Used

d/dy(∫₀ʸ f(t) dt) = f(y)

dy/dx = 1/(dx/dy)

d²y/dx² = d/dy(dy/dx) * dy/dx

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