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Differentiate x^(sinx), x >0w.r.t. x....

Differentiate `x^(sinx), x >0`w.r.t. x.

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To differentiate the function \( y = x^{\sin x} \) with respect to \( x \), we can follow these steps: ### Step 1: Take the natural logarithm of both sides We start with the equation: \[ y = x^{\sin x} \] Taking the natural logarithm on both sides gives: ...
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NCERT ENGLISH-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Prove that the function defined by f(x) = t a n xis a continuous func...

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  2. Examine whether the function f given by f(x)=x^2is continuous at x = ...

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  3. Discuss the continuity of the function f given by f(x) = |x| a t x = 0...

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  4. Check the continuity of the function f given by f(x) = 2x + 3 a t x =...

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  5. Prove that the identity function on real numbers given by f(x) = xis ...

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  6. Is the function defined by f(x) = |x|, a continuous function?

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  7. Show that the function f given by f(x)={x^3+3ifx!=0 1ifx=0is not co...

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  8. Check the points where the constant function f(x) = k is continuous.

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  9. Discuss the continuity of the function/given by f(x)=x^3+x^2-1.

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  10. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

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  11. If y= A sin x+ B cos x, then prove that (d^2y)/(dx^2)+y=0.

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  12. Find (d^2y)/(dx^2), if y=x^3+tanx.

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  13. Find (dy)/(dx), if x^(2/3)+y^(2/3)=a^(2/3).

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  14. Find (dy)/(dx), if x=a(theta+sintheta), y=1(1-costheta).

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  15. Find (dy)/(dx), if x=a t^2, y=2a t.

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  16. Find (dy)/(dx), if x=acostheta,y=asintheta.

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  17. Find (dy)/(dx), if y^x+x^y+x^x=a^b.

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  18. Differentiate x^(sinx), x >0w.r.t. x.

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  19. Differentiate a^xw.r.t. x, where a is a positive constant.

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  20. Differentiate sqrt(((x-3)(x^2+4))/(3x^2+4x+5)) w.r.t x.

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