Đáp án:
$\dfrac{-6(1+\sqrt{x})^{11}}{x^{7}}\\ $
Giải thích các bước giải:
$\dfrac{\dfrac{12(1+\sqrt{x})^{11}x^6}{2\sqrt{x}}-\dfrac{2\sqrt{x}(1+\sqrt{x})^{12}.6x^5}{2\sqrt{x}}}{x^{12}}\\
=\dfrac{12(1+\sqrt{x})^{11}x^6-2\sqrt{x}(1+\sqrt{x})^{12}.6x^5}{x^{12}.2\sqrt{x}}\\ \\
=\dfrac{2x^5\left [6(1+\sqrt{x})^{11}x-\sqrt{x}(1+\sqrt{x})^{12}.6 \right ]}{x^{12}.2\sqrt{x}}\\ \\
=\dfrac{\left [6(1+\sqrt{x})^{11}x-\sqrt{x}(1+\sqrt{x})^{12}.6 \right ]}{x^{7}.\sqrt{x}}\\ \\
=\dfrac{6\sqrt{x}(1+\sqrt{x})^{11}\left [\sqrt{x}-(1+\sqrt{x}) \right ]}{x^{7}.\sqrt{x}}\\ \\
=\dfrac{6(1+\sqrt{x})^{11}\left [\sqrt{x}-1-\sqrt{x} \right ]}{x^{7}}\\ \\
=\dfrac{-6(1+\sqrt{x})^{11}}{x^{7}}\\ $
