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# If $\mathrm{y}={\mathrm{x}}^{\mathrm{x}}+{\mathrm{x}}^{7}+{7}^{\mathrm{x}}+{7}^{7},$ then $\frac{\mathrm{dy}}{\mathrm{dx}}=$

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a
$\mathrm{x}.{\mathrm{x}}^{\mathrm{x}-1}+7{\mathrm{x}}^{6}+\mathrm{x}{7}^{\mathrm{x}-1}$
b
${\mathrm{x}}^{\mathrm{x}}\left(1+{\mathrm{log}}_{\mathrm{e}}\mathrm{x}\right)+7{\mathrm{x}}^{6}+{7}^{\mathrm{x}}\left({\mathrm{log}}_{\mathrm{e}}7\right)$
c
${\mathrm{x}}^{\mathrm{x}}\left(1+{\mathrm{log}}_{\mathrm{e}}\mathrm{x}\right)+7{\mathrm{x}}^{6}+\mathrm{x}.{7}^{\mathrm{x}-1}$
d
$\mathrm{x}.{\mathrm{x}}^{\mathrm{x}-1}{\mathrm{log}}_{\mathrm{e}}\mathrm{x}+7{\mathrm{x}}^{6}+{7}^{\mathrm{x}}\left({\mathrm{log}}_{7}\mathrm{e}\right)$

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detailed solution

Correct option is B

Given $y={x}^{x}+{x}^{7}+{7}^{x}+{7}^{7}$

Use the formula $\frac{d}{dx}\left({x}^{x}\right)={x}^{x}\left(1+\mathrm{log}x\right)$ to differentiate the above function

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