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- Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x...
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- If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) ...
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- If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot
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- Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...
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- If f(x)=x|x|, then prove that f^(prime)(x)=2|x|
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- A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...
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- If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...
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- If x=logp and y=1/p ,then (a)(d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2...
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- If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...
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- Let y=ln(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...
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- Find (dy)/(dx)"for"y=xsinxlogxdot
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- If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...
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- Differentiate y=(e^x)/(1+sinx)
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- Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...
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- lf y=sqrt((1-x)/(1+x)) find dy/dxand prove that (1-x^2)(dy)/(dx)+y=0
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- If g(x)=(f(x))/((x-a)(x-b)(x-c)),where f(x) is a polynomial of degree ...
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- If f(x) = cosx. cos2x. Cos4x. Cos8x.cos16x, then f '(pi/4) is :
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- f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,Pn be th...
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- If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...
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- If d/(dx)[(x^m-A1x^(m-1)+A2x^(m-2)-.......+(-1)^m Am)e^x]=x^m e^x , f...
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