If x^y=e^(x-y) , prove that (dy)/(dx)=(l...

If `x^y=e^(x-y)` , prove that `(dy)/(dx)=(logx)/((1+logx)^2)`

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If x^(y)=e^(x-y) then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

If ylog x=(x-y) , prove that (dy)/(dx)=(logx)/((1+logx)^(2))

if x^(y)=e^(x-y) then prove that (dy)/(dx)=(log_(e)x)/((1+log_(e)x)^(2))

If x^y= y^x , prove that (dy)/(dx)=((y/x-logy))/((x/y-logx))

y=x^(logx)+(logx)^(x)

If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1)) or,(dy)/(dx)+e^(y-x)=0

x(dy)/(dx)=y(logy-logx+1)

If (x^(x)+y^(x))=1," show that "(dy)/(dx)=-{(x^(x)(1+logx)+y^(x)(logy))/(xy^(x-1))}

Solve x(dy)/(dx)=y(logy-logx+1)

"If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y(logx)(logy)]).

CBSE COMPLEMENTARY MATERIAL-CONTINUITY AND DIFFERENTIABILTY-4 Marks Questions

If x^m y^n=(x+y)^(m+n) , prove that (dy)/(dx)=y/x .
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If (x-y)dot(x-y)/x=a , Prove that y(dy)/(dx)+x=2ydot
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If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .
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If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...
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Differentiate sin^(-1){(2^(x+1). 3^x)/(1+(36)^x)}"w i t hr e s p e...
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If sqrt(1-x^6)+sqrt(1-x^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2)...
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If f(x)=sqrt(x^2+1),\ \ g(x)=(x+1)/(x^2+1) and h(x)=2x-3 , then find f...
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If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...
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If x^(y)+y^(x)+x^(x)=m^(n)." then find the value of "(dy)/(dx).
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If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...
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If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin ...
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If x^(2)/a^(2)+y^(2)/b^(2)=1" then show that "(d^(2)y)/(dx^(2))=-b^(4)...
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Verify Rolle's theorem for the function f(x)=e^(x) sin 2x [0, pi/2]
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Verify Lagranges mean value theorem for function f(x)=sqrt(x^2-4) o...
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If Rolle's theorem holds for the function f(x) = x^(3) + bx^(2) + ax +...
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If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0
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Differentiate sin^(-1) [(3x+(4sqrt(1-x^(2))))/(5)] w.r.t.x.
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If x^y=e^(x-y) , prove that (dy)/(dx)=(logx)/((1+logx)^2)
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If f:[-5,5]vecR is differentiable function and iff^(prime)(x) does not...
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If y^(1/n)+y^(-1/n) = 2x then (x^2-1)y2+xy1 is equal to
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