KeytoMatlabExercise7SchoolofMathematicalSciencesXiamenUniversityhttp:/gdjpkc.xmu.edr Key to matlab Exercise 7--calculus > clear; syms yl ux; y1=(l+ur2y(1/2): u exp(-x) >> yl= compose(yl, u, x) Or > clear; syms x: uexp(-x): yl=(1+ur2r(1/2) no recommend yI (1+exp(-x)y2)(1/2) > clear; syms y2 uvx; y2=(1+ur2y(1/2); u=log(v); v=exp(-x) > u x=compose(u, v, x); y2=compose(y2, u x, x) Or > clear; syms y2 uvx; y2=(1+ur2r(1/2); UFlog(v); v=exp(-X) > y2=compose(y2, compose(u, v, x)) > clear; syms x; v=exp(x); LFlog(v); y2=(1+ur2)(1/2) no recommend (1+log(exp(-x)y2)(1/2) > clear; syms y uv wx: y=(l+ur2y(1/2); uFlog(v); v=sin( w); w=exp(-x) >>v x=compose(v, w, x); u x=compose(u, v x, x): y=compose(y, u x, x) Or > clear; syms y uv; y=(l+ur2y(1/2); fLog(v): v=sin( w); w=exp(-x) e(y, compose(u, compose(v, w, x)) > clear; syms x; w=exp(-x); v=sin(w): u=log(v): y=(1+u2r(1/2) no recommend (1+log(sin(exp(-x)^2)(1/2) > clear; syms x y; y=(l+(log(sin(x))2y(1/2) > inverse(y, x) Warning: inverse((1+log(sin(x)2y(1/2) is not unique In sym. inverse at 43 ans asn(exp(-1+x2)(1/2) > clear; syms x u y, y=(x+log(sin(u))r(1/2) > inverse(y ans asin(exp(-X+ur2))Key to MATLAB Exercise 7  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Key to Ex7­1  Key to MATLAB Exercise 7 – Calculus 1.  1) >> clear; syms y1 u x; y1=(1+u^2)^(1/2); u= exp(­x);  >> y1= compose(y1,u,x) Or >> clear; syms x; u=exp(­x); y1=(1+u^2)^(1/2) % no recommend  y1 =  (1+exp(­x)^2)^(1/2) 2) >> clear; syms y2 u v x; y2=(1+u^2)^(1/2); u =log(v); v=exp(­x);  >> u_x=compose(u,v,x); y2=compose(y2,u_x,x) Or >> clear; syms y2 u v x; y2=(1+u^2)^(1/2); u=log(v); v=exp(­x);  >> y2=compose(y2, compose(u, v, x)) Or >> clear; syms x; v=exp(­x); u=log(v); y2=(1+u^2)^(1/2)  % no recommend  y2 =  (1+log(exp(­x))^2)^(1/2) 3) >> clear; syms y u v w x; y=(1+u^2)^(1/2); u=log(v); v=sin(w); w=exp(­x);  >> v_x=compose(v,w,x); u_x=compose(u,v_x,x); y=compose(y,u_x,x) Or >> clear; syms y u v w x; y=(1+u^2)^(1/2); u=log(v); v=sin(w); w=exp(­x);  >> y=compose(y, compose(u, compose(v, w, x))) Or >> clear; syms x; w=exp(­x); v=sin(w); u=log(v); y=(1+u^2)^(1/2)  % no recommend  y =  (1+log(sin(exp(­x)))^2)^(1/2)  2.  1) >> clear; syms x y; y=(1+(log(sin(x)))^2)^(1/2);  >> finverse(y,x) Warning: finverse((1+log(sin(x))^2)^(1/2)) is not unique.  > In sym.finverse at 43  ans =  asin(exp((­1+x^2)^(1/2))) 2) >> clear; syms x u y; y=(x+log(sin(u)))^(1/2);  >> finverse(y,u) ans =  asin(exp(­x+u^2)) 3)