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Differentiate sin^(-1)(3x-4x^3)...

Differentiate `sin^(-1)(3x-4x^3)`

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To differentiate the function \( y = \sin^{-1}(3x - 4x^3) \), we will follow these steps: ### Step 1: Differentiate using the chain rule The derivative of \( y = \sin^{-1}(u) \) where \( u = 3x - 4x^3 \) is given by: \[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - u^2}} \cdot \frac{du}{dx} \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate the following function with respect to x : sin^(-1)(si...

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  2. Differentiate sin^(-1)(2xsqrt(1-x^2))w i t hr e s p e c ttox ,if -1/(...

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  3. Differentiate sin^(-1)(3x-4x^3)

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  4. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

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  5. If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0<x<1 find (dy)/(dx)

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  6. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

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  7. If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

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  8. If y=sqrt(x^2+a^2) ,prove that y(dy)/(dx)-x=0

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  9. If y=xsin^(-1)x+sqrt(1-x^2), p rov et h a t(dy)/(dx)=sin^(-1)x

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  10. If y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x

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  11. If y=e^xcosx ,p rov et h a t(dy)/(dx)=sqrt(2)e^xcos(x+pi/4)

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  12. If y=(x-1)log(x-1)-(x+1)log(x+1),p rov et h a t(dy)/(dx)=log((x-1)/(1+...

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  13. If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

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  14. P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)x/a}=sqrt(a^2-x^...

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  15. If x y=4,p rov et h a tx((dy)/(dx)+y^2)=3y

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  16. Differentiate the following functions with respect to x : tan^(-1)s...

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  17. Differentiate the following functions with respect to x : tan^(-1)((...

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  18. Differentiate the following functions with respect to x : tan^(-1)((3...

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  19. Differentiate the following functions with respect to x : tan^(-1)(...

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  20. Differentiate the following functions with respect to x : tan^(-1){(1+...

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