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If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,...

If `u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v)` is `

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If y="sec"(tan^(-1)x),t h e n (dy)/(dx) at x=1 is (a)cos(pi/4) (b)...

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  2. The differential coefficient of f((log)e x) with respect to x , where ...

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  3. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

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  4. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is ...

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  5. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a)-(cosx+si...

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  6. If x=tcost ,y=t+sint . Then (d^2 x)/(dy^2)at t=pi/2 is (a)(pi+4)/2...

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  7. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) then c is equal to

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  8. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  9. f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x. Also,f(3)=5 and...

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  10. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a)(-2)/(1+x^2) fo...

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  11. Each question contains statements given in two columns which have t...

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  12. Suppose the function f(x) satisfies the relation f(x+y^3)=f(x)+f(y^3)d...

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  13. If for some differentiable function f(alpha)=0a n df^(prime)(alpha)=0,...

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  14. Statement 1: If differentiable function f(x) satisfies the relation f(...

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  15. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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

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  17. dy/dx=(sqrt((1-sin2x)/(1+sin2x))) is equal to, 0ltxltpi/2

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  18. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a)(n y)/(sqrt(x^2+a^2...

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  19. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...

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  20. (d)/(dx)cos^(-1)sqrt(cosx),0ltxlt(pi)/(2) is equal to

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