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- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i35)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- 'diff(y, x) = (y*(x*cos(x)-y-sin(x)))/(x\^{}2 + y*x);
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o35}
- \frac{d}{d x} y=\frac{\left( -y-\sin{(x)}+x \cos{(x)}\right) y}{x y+{{x}^{2}}}\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i27)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- f0(x, y):= y = sin(x)-x*log(y);
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o27}
- \operatorname{f0}\left( x,y\right) :=y=\sin{(x)}-x \log{(y)}\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i28)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- f0(pi/2, 1);
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o28}
- 1=\sin{\left( \frac{pi}{2}\right) }\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i40)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- d: diff(f0(x, y));
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{d}
- \operatorname{del}(y)=\left( \cos{(x)}-\log{(y)}\right) \operatorname{del}(x)-\frac{x \operatorname{del}(y)}{y}\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i43)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- solve(d, del(y))/del(x);
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o43}
- [\frac{\operatorname{del}(y)}{\operatorname{del}(x)}=-\frac{y \log{(y)}-\cos{(x)} y}{y+x}]\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i31)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- f(yp):= yp = (y*(x*cos(x)-y-sin(x)))/(x\^{}2 + y*x);
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o31}
- \operatorname{f}\left( \mathit{yp}\right) :=\mathit{yp}=\frac{y\, \left( x \cos{(x)}-y-\sin{(x)}\right) }{{{x}^{2}}+y x}\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i32)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- f(-(y*log(y)-cos(x)*y)/(y+x));
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o32}
- \frac{\cos{(x)} y-y \log{(y)}}{y+x}=\frac{\left( -y-\sin{(x)}+x \cos{(x)}\right) y}{x y+{{x}^{2}}}\mbox{}
- \]
- %%%%%%%%%%%%%%%
- \noindent
- %%%%%%%%%%%%%%%
- %%% INPUT:
- \begin{minipage}[t]{4em}\color{red}\bf
- (\% i33)
- \end{minipage}
- \begin{minipage}[t]{\textwidth}\color{blue}
- log(y)=y+sin(x);
- \end{minipage}
- %%% OUTPUT:
- \[\displaystyle \tag{\% o33}
- \log{(y)}=y+\sin{(x)}\mbox{}
- \]
- %%%%%%%%%%%%%%%
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