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Differentiate sin^(-1)sqrt(1-x^2) with r...

Differentiate `sin^(-1)sqrt(1-x^2)` with respect to `cos^(-1)x` , if `x∈ [-1,0]`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate cos^(-1)(4x^3-3x) with respect to x' .

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  2. Differentiate sin^(-1)(2xsqrt(1-x^2)),

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  3. Differentiate sin^(-1)sqrt(1-x^2) with respect to cos^(-1)x , if x∈ [-...

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  4. Differentiate sin^(-1)(2a xsqrt(1-a^2x^2)) with respect to sqrt(1-a^2x...

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  5. Differentiate tan^(-1)((1-x)/(1+x)) with respect to sqrt(1-x^2) , if -...

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  6. If f(x)=|[x+a^2 , a b , a c],[a b, x+b^2,b c],[ ac,b c, x+c^2]|. then ...

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  7. If fr(x),gr(x),hr(x),r=1,2,3 are polynomials such that fr(a)=gr(a)=hr...

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  8. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

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  9. If f,g, and h are differentiable functions of x and "delta"=|[f,g,h...

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  10. If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(...

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  11. If f(x)=(log)e((log)e x) , then write the value of f^(prime)(e) .

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  12. If f(x)=x+1 , then write the value of d/(dx)(fof)(x) .

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  13. If f^(prime)(1)=2 and y=f((log)e x) , find (dy)/(dx) at x=e .

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  14. If f(1)=4 , f^(prime)(1)=2 , find the value of the derivative of lo...

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  15. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1...

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  16. Let g(x) be the inverse of an invertible function f(x) which is deri...

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  17. If y=sin^(-1)(sinx) , -pi/2lt=xlt=pi/2 . Then, write the value of (...

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  18. Find dy/dx if x=sin2y

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  19. If pilt=xlt=2pi and y=cos^(-1)(cosx) , find (dy)/(dx) .

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  20. Find dy/dx if x=sin^2y

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