Mathematics, 07.10.2021 01:50 dogsb4doods
Find dy/dx by implicit differentiation. 5y sin(x2) = 3x sin(y2)
Answers: 2
![\dfrac{\mathrm d}{\mathrm dx}\left[5y \sin(x^2)\right] = \dfrac{\mathrm d}{\mathrm dx}\left[3x \sin(y^2)\right] \\\\ 5 \dfrac{\mathrm d}{\mathrm dx}\left[y \sin(x^2)\right] = 3 \dfrac{\mathrm d}{\mathrm dx}\left[x \sin(y^2)\right]](/tpl/images/2493/2220/a9be3.png)
![5 \left(\dfrac{\mathrm d}{\mathrm dx}[y] \sin(x^2) + y \dfrac{\mathrm d}{\mathrm dx}\left[\sin(x^2)\right]\right) = 3 \left(\dfrac{\mathrm d}{\mathrm dx}[x] \sin(y^2) + x \dfrac{\mathrm d}{\mathrm dx}\left[\sin(y^2)\right]\right)](/tpl/images/2493/2220/05c83.png)
![5 \left(\sin(x^2) \dfrac{\mathrm dy}{\mathrm dx} + y \cos(x^2) \dfrac{\mathrm d}{\mathrm dx}\left[x^2\right]\right) = 3 \left(\sin(y^2) + x \cos(y^2) \dfrac{\mathrm d}{\mathrm dx}\left[y^2\right]\right) \\\\ 5 \left(\sin(x^2) \dfrac{\mathrm dy}{\mathrm dx} + 2xy \cos(x^2)\right) = 3 \left(\sin(y^2) + 2xy \cos(y^2) \dfrac{\mathrm dy}{\mathrm dx}\right)](/tpl/images/2493/2220/4e960.png)
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Find dy/dx by implicit differentiation. 5y sin(x2) = 3x sin(y2)...
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