Given the following relations between $x$ and $y$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in t

Question

Given the following relations between $x$ and $y$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$. ${{y}^{x}}=y+x$ $y={{x}^{\text{sec}\hspace{0.5em}x}}$ $y={{x}^{{{x}^{2}}}}$

Accepted Answer

(a) $\frac{y[1-(y+x)\ln y]}{x(y+x)-y}$ (b) $\frac{y\sec x(1+x\tan x\ln x)}{x}$ (c) $x^{x^2+1}(1+2\ln x)$

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

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