Mathematics: Find dy/dx by implicit differentiation. 4 + 7x = sin (xy^2)

D because 2 can go into 2 1 time 6 can go into 2 3 times and also 8 can go into 2 4 times...

Find dy/dx by implicit differentiation. 4 + 7x =

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24kfjkasklfjl

27.07.2019

$4 + 7x = \sin(xy^2)$ answer: $\dfrac{dy}{dx} = \dfrac{7 - y^2\cos(xy^2)}{2xy \cos(xy^2)}$ ======differentiate both sides with respect to x, (we'll be treating y as a function of x)use chain rule for right-hand side: [ f( g(x) ) ]' = f'(g(x) ) · g'(x)thne use product rule for right-hand side: (fg)' = fg' + gf' for convenience, let y' = dy/dx $\begin{aligned} \dfrac{d}{dx}(4 + 7x) & = \dfrac{d}{dx}\sin(xy^2) \\ 0 + 7 & = \cos(xy^2) \cdot \left[x(y^2)' + y^2 x' \right] \\ 7 & = \cos(xy^2) \left[x (2y y') + y^2\cos(xy^2) \right] \\ 7 & = 2xy \cos(xy^2) y' + y^2\cos(xy^2) \\ 7 - y^2\cos(xy^2) & = 2xy \cos(xy^2) y' \\ y' & = \dfrac{7 - y^2\cos(xy^2)}{2xy \cos(xy^2)} \end{aligned}$ therefore, $\dfrac{dy}{dx} = \dfrac{7 - y^2\cos(xy^2)}{2xy \cos(xy^2)}$

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Find dy/dx by implicit differentiation. 4 + 7x = sin (xy^2)

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