Find the $\frac{\mathrm{d}y}{\mathrm{d}x}$ of the following equations in terms of $x$ and $y$:

Question

Find the $\frac{\mathrm{d}y}{\mathrm{d}x}$ of the following equations in terms of $x$ and $y$: $x^{3} + y^{2} + xy = \sin y$ $y^{3} - 2xy = \sin y$ $y = x^{x}$ $x^{2} + 4y^{2} = 3yx$ $5x^{3} - 3y^{3} = 3yx$ $\tan y + x^{2} = x\ln y$ $\cos^{-1}(e^{y}) = x + 2y$

Accepted Answer

(i) $\frac{3x^2+y}{\cos y-x-2y}$ (ii) $\frac{2y}{3y^2-2x-\cos y}$ (iii) $x^x(1+\ln x)$ (iv) No real derivative is determined: the locus consists only of $(0,0)$. (v) $\frac{5x^2-y}{x+3y^2}$ (vi) $\frac{y(\ln y-2x)}{y\sec^2y-x}$ (vii) $-\frac{\sin(x+2y)}{e^y+2\sin(x+2y)}$

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

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