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y=tan x+sec x. Prove that (d^2y)/(dx^2)=...

y=tan x+sec x. Prove that `(d^2y)/(dx^2)=cosx/((1+sinx)^2`.

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Consider y=tan^-1((sqrt(1+x^2)-1)/x). Find dy/dx.

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  2. y=tan x+sec x. Find dy/dx.

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  3. y=tan x+sec x. Prove that (d^2y)/(dx^2)=cosx/((1+sinx)^2.

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  4. If y=sin^-1((sqrt(1+x)+sqrt(1-x))/2) Find dy/dx.

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  5. If y=sin^-1((sqrt(1+x)+sqrt(1-x))/2) Find dy/dx.

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  6. u=(sinx)^(tanx),v=(cosx)^(secx). Find (du)/dxand(dv)/dx.

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  7. u=(sinx)^(tanx),v=(cosx)^(secx) Find dy//dx. if y=(sinx)^(tanx)+(cosx)...

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  8. Given that y=asin nx+b cos nx. Computedy/dx

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  9. Given that y=asin nx+b cos nx. Compute(d^2y)/dx^2

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  10. Given that y=asin nx+b cos nx. Show that(d^2y)/dx^2+n^2y=0.

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  11. Differentiate sin(x^2/3-1) with respect to x.

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  12. Differentiate log{sin(x^2/3-1)} with respect to x.

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  13. Differentiate sqrt(log{sin(x^2/3-1)} with respect to x.

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  14. Consider y=(xsin^-1x)/(sqrt(1-x^2)) Differentiate x. sin^-1x with resp...

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  15. Verify mean value theorem for the function f(x)=(x-2)^2 in [1,4] .

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  16. Find a point on the curve y=(x-2)^2 at which the tangent is parallel t...

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  17. If y=sin(m sin^-1x), Find dy/dx.

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  18. If y=sin(m sin^-1x). Show that sqrt(1-x^2)dy/dx=mcos(msin^-1x)

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  19. If y=sin(m sin^-1x), Hence prove that (1-x^2)(d^2y)/dx^2-xdy/dx+m^2y=0...

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  20. Verify Lagrange 's mean value theorem, if f(x)=x^3-5x^2-3x in the inte...

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