Find dy/dx in terms of $$ x \& y $$ : $$ \begin{array}{l} ext { 1. } x y-x+2 y=1 \ ext { 2. } x^{3}+y^{3}=1 \ ext { 3. } x^{2}+x y=y^{3} \ ext { 4. } x^{3} y+x y^{5}=2 \ ext { 5. } x^{2} y^{3}=2 x-y \ ext { 6. } x^{2}+4(y-1)^{2}=4 \ ext { 7. } \frac{x-y}{x+y}=\frac{x^{2}}{y}+1\end{array} $$

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Find dy/dx in terms of $$ x \& y $$ : $$ \begin{array}{l}	ext { 1. } x y-x+2 y=1 \ 	ext { 2. } x^{3}+y^{3}=1 \ 	ext { 3. } x^{2}+x y=y^{3} \ 	ext { 4. } x^{3} y+x y^{5}=2 \ 	ext { 5. } x^{2} y^{3}=2 x-y \ 	ext { 6. } x^{2}+4(y-1)^{2}=4 \ 	ext { 7. } \frac{x-y}{x+y}=\frac{x^{2}}{y}+1\end{array} $$

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Calculate or simplify the expression $$ \sin(45) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sin\left(45ight)$$
Calculate or simplify the expression $$ \cos(\pi/4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\cos\left(\frac{\pi }{4}ight)$$
- step1: Calculate the trigonometric value:
  $$\frac{\sqrt{2}}{2}$$
Calculate or simplify the expression $$ \sin(45)/\cos(\pi/4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\sin\left(45ight)}{\cos\left(\frac{\pi }{4}ight)}$$
- step1: Transform the expression:
  $$\frac{2\sin\left(45ight)}{\sqrt{2}}$$
- step2: Multiply by the Conjugate:
  $$\frac{2\sin\left(45ight)	imes \sqrt{2}}{\sqrt{2}	imes \sqrt{2}}$$
- step3: Multiply the numbers:
  $$\frac{2\sqrt{2}	imes \sin\left(45ight)}{\sqrt{2}	imes \sqrt{2}}$$
- step4: Multiply the numbers:
  $$\frac{2\sqrt{2}	imes \sin\left(45ight)}{2}$$
- step5: Reduce the fraction:
  $$\sqrt{2}	imes \sin\left(45ight)$$
The value of $$ \frac{\sin(45^{\circ})}{\cos(\frac{\pi}{4})} $$ is $$ \sqrt{2} $$.
$$ \sqrt{2} $$.

Find dy/dx in terms of :

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