Class 12- Differentiation-if y=log(root x +1/ root x), prove that dy/dx= x-1/2x(x+1)

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If y=log(root x+1/root x)^2 then prove that x(x+1)^2 d2y/dx2 + (x+1)^2 dy/dx = 2 / Differentiation If y=log(root x+1/root x)^2 then prove that x(x+1)^2 d2y/dx2 + (x+1)^2 dy/dx = 2 / Differentiation
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Q25. If y=log⁑√(1+tan⁑x)/(1-tan⁑x ) , Prove that dy/dx= sec^2x. Q25. If y=log⁑√(1+tan⁑x)/(1-tan⁑x ) , Prove that dy/dx= sec^2x.
If `y=log(sqrt(x)+1/sqrt(x))`. Prove that `dy/dx=(x-1)/(2x(x+1))` If `y=log(sqrt(x)+1/sqrt(x))`. Prove that `dy/dx=(x-1)/(2x(x+1))`
If y√(x^2+1) = log(√x^2+1)-x), show that (x^2+1)dy/dx+xy+1=0 / Differentiation Class 12 Maths If y√(x^2+1) = log(√x^2+1)-x), show that (x^2+1)dy/dx+xy+1=0 / Differentiation Class 12 Maths
If 𝑦=(log(π‘₯+√(1+π‘₯^2 )))^2, prove that (1+π‘₯^2 ) (𝑑^2 𝑦)/(𝑑π‘₯^2 )+π‘₯ 𝑑𝑦/𝑑π‘₯=2 #cbse2026 #maths #cbse If 𝑦=(log(π‘₯+√(1+π‘₯^2 )))^2, prove that (1+π‘₯^2 ) (𝑑^2 𝑦)/(𝑑π‘₯^2 )+π‘₯ 𝑑𝑦/𝑑π‘₯=2 #cbse2026 #maths #cbse
if xsqrt(1+y)+ysqrt(1+x)=0 for x E (-1,1) then prove that dy/dx=-1/(1+x)^2 if xsqrt(1+y)+ysqrt(1+x)=0 for x E (-1,1) then prove that dy/dx=-1/(1+x)^2
Q) If 𝑦=lo𝑔(√π‘₯+1/√π‘₯)^2, then show that π‘₯(π‘₯+1)^2 𝑦_2+(π‘₯+1)^2 𝑦_1=2 CBSEPYQ2025 #cbse2026#cbseclass12 Q) If 𝑦=lo𝑔(√π‘₯+1/√π‘₯)^2, then show that π‘₯(π‘₯+1)^2 𝑦_2+(π‘₯+1)^2 𝑦_1=2 CBSEPYQ2025 #cbse2026#cbseclass12