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BANSAL-LIMITS AND DERIVATIVES-All Questions
- Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...
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- Find (dy)/(dx) , if x=a(cost+logtant/2) , y=asint
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- Find (dy)/(dx) , if x=asectheta , y=btantheta
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- Find (dy)/(dx) , if x=a(costheta+thetasintheta) , y=a(sintheta-thetaco...
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- If x=sqrt(a^sin^((-1)t)) , y=sqrt(a^cos^((-1)t)) , show that (dy)/(...
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- If y = x^3 + tan x, show that (d^2y)/dx^2= 6x + 2 sec^2 tanx.
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- If y=3e^(2x)+2e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .
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- If y=sin^(-1)x , show that (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .
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- If y=5cosx-3sinx , prove that (d^2y)/(dx^2)+y=0 .
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- If y=3cos(logx)+4sin(logx) , show that x^2y2+x y1+y=0
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- If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...
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- If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2
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- If y=(tan^(-1)x)^2 , show that (x^2+1)^2y2+2x(x^2+1)y1=2 .
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- For a positive constant a find (dy)/(dx) , where y=a^(t+1/t) and x=(t+...
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- Differentiate sin^2x w.r.t. e^(cosx) .
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- Find (dy)/(dx) , if y=12(1-cost) , x=10(t-sint)
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- Find (dy)/(dx) , if y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , -1lt=xlt=1
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- If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)
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- If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+...
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- If x=a(cost+tsint) and y=a(sint- tcost) , find (d^2y)/(dx^2) .
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