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If sin(x y)+y/x=x^2-y^2 , find (dy)/(dx)...

If `sin(x y)+y/x=x^2-y^2` , find `(dy)/(dx)` .

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AI Generated Solution

To find \(\frac{dy}{dx}\) for the equation \( \sin(xy) + \frac{y}{x} = x^2 - y^2 \), we will use implicit differentiation. Here’s a step-by-step solution: ### Step 1: Differentiate both sides of the equation We start with the equation: \[ \sin(xy) + \frac{y}{x} = x^2 - y^2 \] We differentiate both sides with respect to \(x\). ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=xsiny , prove that (dy)/(dx)=(siny)/((1-xcosy))

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  2. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

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  3. If sin(x y)+y/x=x^2-y^2 , find (dy)/(dx) .

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  4. If tan(x+y)+tan(x-y)=1 , find (dy)/(dx) .

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  5. If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) o...

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  6. If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+y))...

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  7. If y={(log)(cosx)sinx}{(log)(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),f...

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  8. If sqrt(y+x) +sqrt(y-x) =c show that dy/dx = y/x -sqrt((y^2/x^2)-1)

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  9. Differentiate the following functions with respect to x : (I)x^x (ii...

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  10. Differentiate (sinx)^(logx) with respect to x :

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  11. Differentiate (cosx)^x with respect to x :

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  12. Differentiate x^(sqrt(x)) with respect to x :

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  13. Differentiate x^(x^x) + (logx)^(sinx) with respect to x :

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  14. Differentiate (sinx)^(cosx) with respect to x :

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  15. Differentiate x^cos^((-1)x) with respect to x :

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  16. Differentiate (sinx)^cos^((-1)x) with respect to x :

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  17. Differentiate (x)^(x^x) with respect to x :

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  18. Differentiate (x^x)^x with respect to x :

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  19. If y=(sinx)^(tanx)+(cosx)^(secx) , find (dy)/(dx)

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  20. Differentiate: (logx)^x+x^(logx) with respect to xdot

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