differentiation

Related Questions

• If ${{f}_{n}}(x)$, ${{g}_{n}}(x)$, ${{h}_{n}}(x),n=1,\,2,\,3$are polynomials in x such that ${{f}_{n}}(a)={{g}_{n}}(a)={{h}_{n}}(a),n=1,2,3$ and $F(x) = \begin{vmatrix} {{f_1}(x)}&{{f_2}(x)}&{{f_3}(x)}\\ {{g_1}(x)}&{{g_2}(x)}&{{g_3}(x)}\\ {{h_1}(x)}&{{h_2}(x)}&{{h_3}(x)} \end{vmatrix}$. Then ${F}'(a)$is equal to

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• On the interval $\left( 0,\frac{\pi }{2} \right)$, the function log sin x is

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• If $u={{x}^{2}}{{\tan }^{-1}}\frac{y}{x}-{{y}^{2}}{{\tan }^{-1}}\frac{x}{y}$, then $\frac{{{\partial }^{2}}u}{\partial x\,\partial \,y}=$

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• If $y = \frac{{{{(1 - x)}^2}}}{{{x^2}}}$, then $\frac{{dy}}{{dx}}$is

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• If $y = {\left( {1 + \frac{1}{x}} \right)^x}$, then $\frac{{dy}}{{dx}} = $

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