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2 апреля 2023 05:24
477
Найдите производную функции1) y= корень 3 степени из 8x
2) y= 1/2 корень 3 степени из x^-2
3) y= 2/x^3
4) y=2/корень из x
5) y= 1/корень 3 степени из x
6) y= 6/ корень 3 степени из x^2
7) y= 1/ корень из 4x^3
8) y= 1/ корень из x^2/3
1
ответ
197–ой:
1.
;
2.
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3.
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4.![(\sqrt[3])'=(x^{\frac})'=\fracx^{-\frac}](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7Bx%5E2%7D%29%27%3D%28x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%27%3D%5Cfrac%7B2%7D%7B3%7Dx%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D "(\sqrt[3])'=(x^{\frac})'=\fracx^{-\frac}")
;
5.![(\sqrt[3])'=(2\sqrt[3])'=2*(x^{\frac})'=2*\fracx^{-\frac}=\fracx^{-\frac}](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B8x%7D%29%27%3D%282%5Csqrt%5B3%5D%7Bx%7D%29%27%3D2%2A%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%27%3D2%2A%5Cfrac%7B1%7D%7B3%7Dx%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Cfrac%7B2%7D%7B3%7Dx%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D "(\sqrt[3])'=(2\sqrt[3])'=2*(x^{\frac})'=2*\fracx^{-\frac}=\fracx^{-\frac}")
;
6.![(\frac\sqrt[3]})'=\frac*(x^{-\frac})'=\frac*(-\fracx^{-\frac})=-\fracx^{-\frac}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%5Csqrt%5B3%5D%7Bx%5E%7B-2%7D%7D%29%27%3D%5Cfrac%7B1%7D%7B2%7D%2A%28x%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%29%27%3D%5Cfrac%7B1%7D%7B2%7D%2A%28-%5Cfrac%7B2%7D%7B3%7Dx%5E%7B-%5Cfrac%7B5%7D%7B3%7D%7D%29%3D-%5Cfrac%7B1%7D%7B3%7Dx%5E%7B-%5Cfrac%7B5%7D%7B3%7D%7D "(\frac\sqrt[3]})'=\frac*(x^{-\frac})'=\frac*(-\fracx^{-\frac})=-\fracx^{-\frac}")
.
198–ой:
1.
;
2.
;
3.![(\frac{\sqrt[3]})'=-\frac})'}{(x^{\frac})^2}=-\frac\frac}}}}=-\fracx^{-\frac}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D%29%27%3D-%5Cfrac%7B1%2A%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%27%7D%7B%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%5E2%7D%3D-%5Cfrac%7B1%7D%7B3%7D%5Cfrac%7Bx%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%7D%7Bx%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%3D-%5Cfrac%7B1%7D%7B3%7Dx%5E%7B-%5Cfrac%7B4%7D%7B3%7D%7D "(\frac{\sqrt[3]})'=-\frac})'}{(x^{\frac})^2}=-\frac\frac}}}}=-\fracx^{-\frac}")
;
4.![(\frac{\sqrt[3]})'=-\frac})'}{(x^{\frac})^2}=-\frac}}}}=-4x^{-\frac}](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%7D%7B%5Csqrt%5B3%5D%7Bx%5E2%7D%7D%29%27%3D-%5Cfrac%7B6%2A%28x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%27%7D%7B%28x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E2%7D%3D-%5Cfrac%7B4x%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D%7Bx%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%7D%3D-4x%5E%7B-%5Cfrac%7B5%7D%7B3%7D%7D "(\frac{\sqrt[3]})'=-\frac})'}{(x^{\frac})^2}=-\frac}}}}=-4x^{-\frac}")
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5.
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198–ой:
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0
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Хороший ответ
4 апреля 2023 05:24
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