Ответ:
Производная дроби равна [tex]\bf \Big(\dfrac{u}{v}\Big)'=\dfrac{1}{v^2}\cdot (u'v-uv')[/tex] .
[tex]\bf \left(\dfrac{cos\, (e^{10x})\ -\ sin(10x^2)}{tg(sin10x)}\right)'=\\\\\\=\dfrac{1}{tg^2(sin10x)}\cdot \Big(\Big(-sin(e^{10x})\cdot e^{10x}\cdot 10-cos(10x^2)\cdot 20x\Big)\cdot tg(sin10x)-\\\\\\-\Big((cos(e^{10x})-sin(10x^2)\Big)\cdot \dfrac{1}{cos^2(sin10x)}\cdot 10\, cos10x\Big)[/tex]
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Answers & Comments
Ответ:
Производная дроби равна [tex]\bf \Big(\dfrac{u}{v}\Big)'=\dfrac{1}{v^2}\cdot (u'v-uv')[/tex] .
[tex]\bf \left(\dfrac{cos\, (e^{10x})\ -\ sin(10x^2)}{tg(sin10x)}\right)'=\\\\\\=\dfrac{1}{tg^2(sin10x)}\cdot \Big(\Big(-sin(e^{10x})\cdot e^{10x}\cdot 10-cos(10x^2)\cdot 20x\Big)\cdot tg(sin10x)-\\\\\\-\Big((cos(e^{10x})-sin(10x^2)\Big)\cdot \dfrac{1}{cos^2(sin10x)}\cdot 10\, cos10x\Big)[/tex]