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If x sin (a+y) + sin a cos (a+y) = 0, th...

If x sin (a+y) + sin a cos (a+y) = 0, then prove that : `dy/dx = (sin^2(a+y))/(sina)`

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If sin y = x sin (a + y), then prove that (dy)/(dx) = (sin^(2) (a + y))/(sin a) .

If sin y = x cos (a + y) , prove that (dy)/(dx) = (cos^2 (a + y))/(cos a)

If x cos (a+y) = cos y, then prove that dy/dx = (cos^2(a+y))/(sina) Hence, show that sina(d^2y)/(dx^2)+ sin 2(a+y) (dy)/(dx) = 0

If y = x sin(a+y), prove that dy/dx = (sin^2(a+y))/(sin(a+y)-ycos(a+y))

If siny = xsin(a+y) , prove that dy/dx=sin^2(a+y)/sina

If cosy = xcos(a+y) , with cos a ne +-1 , prove that dy/dx = (cos^2(a+y))/sina

If y = x sin y, prove that x dy/dx = y/(1-x cosy)

If x cos (a + y)=cos y then prove that [dy/dx = cos^2 (a+ y) /sin a] . Hence show that [sin a (d^2y /dx^2) + sin 2(a+ y) dy/dx =0] .

ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. Find (dy)/(dx), if y^(x) + x^(y) +x^(x) = a^(b).

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  2. If y=asinx+bcosx, prove thaty^2+((dy)/(dx))^2=a^2+b^2

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  3. If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^...

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  4. Find the value of (dy)/(dx) at theta=(pi)/(4) if x=ae^(theta)(sintheta...

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  5. If x=cost(3-2cos^(2)t) and y=sint(3-2sin^(2)t), find the value of (dy)...

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  6. If x=asin2t(1+cos2t)" and "y=bcos2t(1-cos2t). show that ((dy)/(dx))(t=...

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  7. Find (dy)/(dx) at t=(pi)/(4),(pi)/(3), when x=a(cost+log"tan"(t)/(2)),...

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  8. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that" (dy...

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  9. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), find (dy)/(dx).

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  10. Find dy/dx when : y = x^(cotx) +(2x^2-3)/(x^2+x+2)

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  11. Find (dy)/(dx), if y=(cosx)^(x)+(sinx)^((1)/(x)).

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  12. If (cosx)^(y)=(siny)^(x), then find (dy)/(dx).

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  13. If y=x^(cotx)+(sinx)^(x), find (dy)/(dx).

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  14. Differentiate (sinx)^(x)+(cosx)^(sinx) w.r.t. x.

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  15. Differentiate sin^-1(2^(x+1)/(1+4^x)) w.r.t x

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  16. Differentiate the following with respect to x: sin^-1[(2^(x+1).3^x)/...

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  17. If y=cos^(-1)((2^(x+1))/(1+4^(x))), find (dy)/(dx).

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  18. If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , pr...

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  19. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  20. If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

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