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Find the derivatives of the following : ...

Find the derivatives of the following :
`y=x^(cosx)`

Text Solution

Verified by Experts

The correct Answer is:
`x^(cosx)[cosx/x - (logx)(sinx)]`
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PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -SOLUTION TO EXERCISE 10.4
  1. Find the derivatives of the following : y=x^(cosx)

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  2. Find the derivatives of the following : y=x^(logx)+(logx)^(x)

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  3. Find the derivatives of the following : sqrt(xy)=e^((x-y))

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  4. Find the derivatives of the following : x^(y)=y^(x)

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  5. Find the derivatives of the following : (cosx)^(logx)

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  6. Find the derivatives of the following : x^(2)/a^(2)+y^(2)/b^(2)=1

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  7. Find the derivatives of the following : sqrt(x^(2)+y^(2))=tan^(-1)(y...

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  8. Find the derivatives of the following : tan(x+y)+tan(x-y)=x

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  9. if cos(xy)=x, show that (dy)/(dx)=(-(1+ysin(xy)))/(xsinxy).

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  10. Find the derivatives of the following : tan^(-1)sqrt((1-cosx)/(1+cos...

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  11. Find the derivatives of the following : tan^(-1)((6x)/(1-9x^(2)))

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  12. Find the derivatives of the following : cos(2tan^(-1)sqrt((1-x)/(1+x...

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  13. Find the derivatives of the following : x=acos^(3)t, y=asin^(3)t

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  14. Find the derivatives of the following : x=a(cost+tsint), y=a(sint-tc...

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  15. Find the derivatives of the following : x=(1-t^(2))/(1+t^(2)), y=(2t...

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  16. Find the derivatives of the following : cos^(-1)((1-x^(2))/(1+x^(2))...

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  17. Find the derivatives of the following : sin^(-1)(3x-4x^(3))

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  18. Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-s...

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  19. Find the derivative of sinx^(2) with respect to x^(2).

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  20. Find the derivative of sin^(-1)((2x)/(1+x^(2))) with respect to tan^(-...

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