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Differentiate (e^(x)cos x+x^(2)"log"x) ...

Differentiate `(e^(x)cos x+x^(2)"log"x)`
with respect to 'x'.

Text Solution

Verified by Experts

Let `y=e^(x)cos x+x^(2)"log"x`
`rArr (dy)/(dx)=(d)/(dx)(e^(x)cos x+x^(2)"log"x)`
`=(d)/(dx)(e^(x)cos s)+(d)/(dx)(x^(2)"log"x)`
`=e^(x)(d)/(dx)c os x+cos x(d)/(dx)e^(x)`
`+x^(2)(d)/(dx)"log"x+log"x(d)/(dx)x^(2)`
`=-e^(x)sin x+cos x.e^(x)`
`+x^(2).(1)/(x)+"log"x.(2x)`
`=e^(x)(cos x-sinx)+x+2x"log"x`
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NAGEEN PRAKASHAN-LIMITS AND DERIVATIVES-Miscellaneous Exercise
  1. Differentiate (e^(x)cos x+x^(2)"log"x) with respect to 'x'.

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  2. Find the derivative of the following functions from first principles:...

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  3. Find the derivative of the following functions (it is to be understand...

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  4. Find the derivative of the following functions (it is to be understand...

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  5. Find the derivative of the following functions (it is to be understand...

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  6. Find the derivative of the following functions (it is to be understand...

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  7. Find the derivative of the following functions (it is to be understand...

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  8. Find the derivative of the following functions (it is to be understand...

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  9. Find the derivative of the following functions (it is to be understand...

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  10. Find the derivative of the following functions (it is to be understand...

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  11. Find the derivative of the following functions (it is to be understand...

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  12. Find the derivative of the following functions (it is to be understand...

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  13. Find the derivative of the following functions (it is to be understand...

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  14. Find the derivative of the following functions (it is to be understand...

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  15. Find the derivative of the following functions (it is to be understand...

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  16. Find the derivative of the following functions (it is to be understand...

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  17. Find the derivative of the following functions (it is to be understand...

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  18. Find the derivative of the following functions (it is to be understand...

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  19. Find the derivative of the following functions (it is to be understand...

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  20. Find the derivative of the following functions (it is to be understand...

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  21. Find the derivative of the following functions (it is to be understand...

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