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" 13.If "y=x-(x^(2))/(2)+(x^(3))/(3)-(x^...

" 13.If "y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+cdots," prove that "(1+x)(dy)/(dx)=1

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If y = x- (x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+* * * prove that (1 + x) (dy)/(dx) = 1

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+ . . .+(x^(n))/(n!) , prove that (dy)/(dx)+(x^(n))/(n!)=y

If y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * *infty show that (dy)/(dx) = y

If y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * * +(x^(n))/(n!) prove that (dy)/(dx) + (x^(n))/(n!)=y*

If y= 1+ x + (x^2)/( 2!) + (x^3)/( 3!) + (x^4)/(4!) +…. to oo , show that (dy)/( dx) = y .

If y=(x)/(sqrt(1+x^(2))) , prove that, x^(3)(dy)/(dx)=y^(3) .

If xy=4, prove that x((dy)/(dx)+y^(2))=3y

If xy=4, prove that x((dy)/(dx)+y^(2))=3y

If xy=4, prove that x((dy)/(dx)+y^(2))=3y

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+...oo, then find the value of (dy)/(dx) .