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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
- Find the derivative of tan^(-1)(cos^2x).
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- Examine the differentiability of ln x^(2) for all real values of x.
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- Find (dy)/(dx) when y=tan^(-1) ((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x)...
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- Differentiate sin^(-1) ((2X)/(1+X^(2))) with respect to cos^(-1) ((1-X...
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- Find (dy)/(dx) wheny=x^y.
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- If 2z=x(2+(dz)/(dx)), then prove that (d^(2)z)/(dx^(2)) is a constant.
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- If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2
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- If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...
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- If (cosx)^(y)=(cosy)^(x), then find (dy)/(dx).
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- If x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t)), then show that (dy)/(d...
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- Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t x.
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- If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((d...
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- If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)
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- If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...
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- If x= cos t+ log tan t/2 and y = sin t, then find the value of (d^2y)/...
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- If xsqrt(1+y)+ysqrt(1+x)=0 for -1ltx,ylt1 then prove that (dy)/(dx)=(-...
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- If x=tan(1/a logy), show that (1+x^2)d^2y/dx^2+(2x-a)dy/dx=0.
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- Differentiate the following function w.r.tx tan^(-1)((sqrt(1+x)-sqrt(1...
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- If y=sin^(-1)[((5x+12(sqrt(1-x^2)))/13)] then find (dy)/(dx).
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- If y=tan(x+y), then find (dy)/(dx).
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