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Differentiate the following functions w....

Differentiate the following functions w.r.t. t :
`(t^(-2)+t^(2))(2^(t)-3^(t))`

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The correct Answer is:
`(t^(-2)+t^(2))(2^(t)log2-3^(t)log3)+2(2^(t)-3^(t))(t-t^(-3))`
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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Find (dy)/(dx) when : y=(x+2)/((x-1)(x+5))

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  2. Differentiate the following functions w.r.t. t : (3^(t) cos t+sin t...

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  3. Differentiate the following functions w.r.t. t : (t^(-2)+t^(2))(2^(...

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  4. Differentiate the following functions w.r.t. t : sqrt(t) e^(t) sec...

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  5. Differentiate the following functions w.r.t. t : (u)/( e^(u) -1)

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  6. Differentiate the following functions w.r.t. t : (u sin u+cos u)/(u...

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  7. If x=a(theta+sin theta) and y=a(1+cos theta), then find the simplified...

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  8. If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)), show...

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  9. Find the differential coefficient of : (tan^(-1)x)/(1+tan^(-1)x)" ...

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  10. Find the differential coefficient of : "tan"^(-1)(sqrt(1+x^(2))-1)/...

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  11. Find the differential coefficient of : "cos"^(-1)(1-x^(2))/(1+x^(2...

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  12. Find the differential coefficient of : x^(sin^(-1)x)" w.r.t. " sin...

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  13. If y=(x)/(sqrt(1+x^(2))), prove that, x^(3)(dy)/(dx)=y^(3).

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  14. If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)).

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  15. If ye^(y)=x, prove that, (dy)/(dx)=(y)/(x(1+y)).

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  16. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), show that, (dy)/(dx)=(sqrt(1-...

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  17. If y= e^(sin^(-1)x) and z=e^(-cos^(-1)x), prove that the value of (dy...

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  18. If y=sin((pi)/(6)e^(xy)), find (dy)/(dx) at x=0.

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  19. If y=x^(x^(x^(...oo))), then prove that, (dy)/(dx)=(y^(2))/(x(1-y lo...

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  20. If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo), show that, x (dy)/(dx)...

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