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If y=|f(x)g(x)h(x)l m n a b c| , prove t...

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

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

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

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

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

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

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

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

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

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

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  11. Find dy/dx if x=sin2y

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

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

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  14. If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , wr...

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  15. If y=x|x| , find (dy)/(dx) for x<0 .

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  16. If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

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  17. If x=a(theta+sintheta),\ \ y=a(1+costheta) , find (dy)/(dx) .

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  18. If y=x^x , find (dy)/(dx) at x=e .

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  19. If y=tan^(-1)((1-x)/(1+x)) , find (dy)/(dx) .

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  20. If y=(log)a x , find (dy)/(dx) .

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