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Question Number 32980 by Nayon.Sm last updated on 08/Apr/18

$$$$$$$$$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\left|\begin{array}{ccc}{({\mathrm{x}}^2+2)}^{{\mathrm{x}}^3+3}& 2^{\mathrm{x}}& {\mathrm{cosx}}^{\mathrm{x}}\\ {\log }_{2^{\mathrm{x}+1}}({\mathrm{x}}^2+{\mathrm{x}}^{2\mathrm{x}}+\stackrel{}{3})& \mathrm{xlnx}& {\sin }^{-1}\mathrm{tanx}\\ 3& {\pi }^{\mathrm{sinhx}}& {\mathrm{e}}^{\mathrm{x}}\end{array}\right|\right)=?$$$$$$

Answered by MJS last updated on 08/Apr/18

$$\left|\begin{array}{ccc}x{(x^2+2)}^{x^3+2}((3x^3+6x)\ln (x^2+2)+2x^3+6)& \ln 2\times 2^x& -\sin x^x\times x^x(1+\ln x)\\ \frac{1}{\ln 2\times (x+1)}(\frac{2((1+\ln x)x^{2x}+x)}{x^{2x}+x^2+3}-\frac{\ln (x^{2x}+x^2+3)}{x+1})& 1+\ln x& \frac{1}{\mid \cos x\mid \sqrt{\cos 2x}}\\ 0& \ln \pi \times \cosh x\times {\pi }^{\sinh x}& e^x\end{array}\right|$$

Commented by Nayon.Sm last updated on 15/Apr/18

$$\mathrm{wron}\stackrel{}{\mathrm{g}}$$

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