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 $y$. $(x - 2y)^{3} - 3\cos(2xy^{5}) = 7$ $(4x^{2} + 3y)^{5} - 5\sin y = 3$ $\tan y-5{{x}^{3}}\cos x=xy$

Accepted Answer

(i) $\frac{-2y^5\sin(2xy^5)-(x-2y)^2}{10xy^4\sin(2xy^5)-2(x-2y)^2}$ (ii) $-\frac{8x(4x^2+3y)^4}{3(4x^2+3y)^4-\cos y}$ (iii) $\frac{y-5x^3\sin x+15x^2\cos x}{\sec^2y-x}$

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

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