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If x = e^(x/y), then show that dy/dx = f...

If x = `e^(x/y)`, then show that dy/dx = `frac{x-y}{x log x}`

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If x^y = e^(x-y) , then show that dy/dx = frac{log x}{(1+ log x)^2}

If y= x^(x^(x...)) , then show that dy/dx = frac{y^2}{x(1-log y)}

If e^y = y^x , then show that dy/dx = frac{(log y)^2}{log y -1}

Solve the following: If x = e^ sin 3t , y= e^cos 3t , then show that dy/dx = - frac{y log x}{x log y}

If e^x + e^y = e^(x+y) , then show that dy/dx = - e^(y-x)

If sqrt (y+x) + sqrt (y-x) = c , then show that dy/dx = frac{y}{x} - sqrt (frac{y^2}{x^2} -1)

If e^x + e^y = e^(x+y) , show that dy/dx = - e^(y-x)

If sin y = x sin(a+y), then show that dy/dx = frac{ sin^2 (a+y)}{sin a}

Solve the following: If x = a cos^(3) t, y= a sin^(3) t, then show that dy/dx = - (frac{y}{x})^(1/3)

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If x = e^(x/y), then show that dy/dx = frac{x-y}{x log x}

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  2. Differentiate the following w.r.t. x : sin(x^2 + x)

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  3. Differentiate the following w.r.t. x : cos(log x)

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  4. Differentiate the following w.r.t. x : cot (x^3)

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  5. Differentiate the following w.r.t. x : log(log x)

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  6. Differentiate the following w.r.t. x : 9^(\log(3) (sin x)) + 25^(log(5...

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  7. Differentiate the following w.r.t x: cos^(-1) (2^x)

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  8. Differentiate the following w.r.t. x: cot^(-1) (frac{1}{x})

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  9. Differentiate the following w.r.t. x: sin^(-1) (2 cos^2 x -1)

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  10. Differentiate the following w.r.t. x: cosec^(-1) frac{1}{3x- 4 x^3}

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  11. Differentiate the following w.r.t. x: sin^(-1) (frac{a sin x + b cos ...

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  12. Differentiate the following w.r.t. x: tan^(-1) (frac{6x}{1+ 16 x^2})

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  13. Differentiate the following w.r.t. x: e^(3x) sin^2 x log x

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  14. Differentiate the following w.r.t. x: (x+1)^(3/2) (2x+3)^(5/2) (3x+4)^...

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  15. Differentiate the following w.r.t. x: x^x + a^a

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  16. Differentiate the following w.r.t. x: (sin x)^(tan x)

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  17. Find dy/dx if, x^2 + e^(xy) = y^2 + log(x+y)

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  18. Find dy/dx if, e^(2x) + e^(2y) = e^(2(x+y))

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  19. If y=1+ xe^y , then show that dy/dx =frac{e^y}{2-y}

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  20. If y=log((1-x^2)/(1+x^2)), then (dy)/(dx) is equal to

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  21. If sqrt (1-x^2) + sqrt (1-y^2) = a(x-y), then show that dy/dx = sqrt...

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