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if cos y=x cos (a+y), (a!= 0) , then sho...

if cos y=x cos (a+y), `(a!= 0)` , then show that `dy/dx= cos ^2(a+y)/sin a`

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If cosy=xcos(a+y),(ane0) , then show that (dy)/(dx)=(cos^2(a+y))/(sina) .

If cosy=x cos(a+y)," prove that " (dy)/(dx) =(cos^(2)(a+y))/(sin a) , where a ne 0 is a constant .

If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y)/(x tan y+log cos x).

If cos y= x cos (a+y) , with cos a ne pm 1 , prove that (dy)/(dx)=(cos^(2)(a+y))/(sin a) .

If xsin^3a+ycos^3a = sin a cos a and x sin a- y cos a = 0 , then show that x^2+y^2= 1 .

If x= cos theta+ I sin theta and y= cos psi + I sin psi , then show that (x)/(y)+(y)/(x)= 2 cos (theta- psi) .

If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(-1)t) then show that (dy)/(dx)=-y/x .

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If y = a cos(logx) + b sin(log x) , show that, x^2(d^2y)/(dx^2)+x(dy)/(dx) + y = 0

If y=cos(2sin^(-1)x) , then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+4y=0

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2...

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  2. Let f: RrarrR be such that f (1) = 3 and f' (1) = 6 Then, lim(xrarr0)(...

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  3. if cos y=x cos (a+y), (a!= 0) , then show that dy/dx= cos ^2(a+y)/sin ...

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  4. Let f(x)=|[x^3,sinx,cosx],[6,-1, 0],[p, p^2,p^3]|, where p is a cons...

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  5. Find (dy)/(dx) for y=sin^(-1)(cosx)

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  6. True or False -The derivative of an even function is always an odd fun...

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  7. If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)) then (dy)/(dx)...

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  8. Let F(x)=f(x)g(x)h(x) for all real x, where f(x),g(x), and h(x) are di...

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  9. Find (dy)/(dx) for y=tan^(-1){(1-cosx)/(sinx)}.

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  10. If x=y+sin^2x then at x=0 ,(dy)/dx=

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  11. f(x)=sin^(-1)(2xsqrt(1-x^2)) then f'(x)=

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  12. If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= for x>20

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  13. Find (dy)/(dx) for y=tan^(-1) sqrt(sec^2x/ (cosec^2x))

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  14. If y=(sinx)^(tanx),t h e n(dy)/(dx)= (a)(sinx)^(tanx)(1+sec^2xlogsi...

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  15. If y=sin^(-1)(sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)

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  16. Suppose that f(x) is a quadratic expresson positive for all real x If ...

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

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  18. If y^2=P(x), where P(x) is a polynomial of degree 3, then 2d/dx(y^3(d^...

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  19. If g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(...

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  20. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of li...

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