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If f,g,a n d \ h are differentiable fu...

If `f,g,a n d \ h` are differentiable functions of `x` and `d(x)=|[f,g,h],[(xf)',(xg)',(x h)'],[(x^(2)f)'',(x^2g)'',(x^2h)'']|` prove that `d^(prime)(x)=|[f,g,h],[f',g',h'],[(x^3f' ')',(x^3g' ')',(x^3h ' ')']|`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
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  8. If x=e^(y+e^(y+e^y....oo) , where x &gt0,then find(dy)/(dx)

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  11. (dy)/(dx) for y=tan^(-1){sqrt((1+cosx)/(1-cosx))} ,where 0 lt x lt pi,...

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  12. If y^x=x^y ,"then find"(dy)/(dx)dot

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  13. Differentiate (xcosx)^x with respect to xdot

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