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Question

If y=(a2+x2)+(a2x2)(a2+x2)(a2x2), then show that
dydx=2a2x3{1+a2(a4x4)}

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Solution

y=a2+x2+a2x2a2+x2a2x2
Multiply numerator and denominator by a2+x2+a2x2

y=(a2+x2+a2x2)2a2+x2(a2x2)

y=(a2+x2)+(a2x2)+2(a4x4)2x2

y=a2x2+(a4x4)x2

dydx=2a2x32(a4x4)x3+1x2.12(a4x4)(4x3)

=2a2x3[1+a2(a4x4)]

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