Differentiate the following equations with respect to $x$: \(x\frac{\mathrm{d}y}{\mathrm{d}x} = \c

Question

Differentiate the following equations with respect to $x$: $x\frac{\mathrm{d}y}{\mathrm{d}x} = \cos(xy) + \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^{2}$ $y\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^{2} = \cos(xy) + \tan z$

Accepted Answer

(i) $xy''+y'=-\sin(xy)(xy'+y)+2y'y''$ (ii) $2yy'y''+(y')^3=-\sin(xy)(xy'+y)+\sec^2z\frac{\mathrm dz}{\mathrm dx}$

Techniques of Differentiation - Higher Derivatives by Implicit Differentiation

Techniques of Differentiation - Higher Derivatives by Implicit Differentiation

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