CRL 4.24 Exercises MrG 2011.1213

3616 days ago by calcpage123

#1) var('a') f(x)=sin(a*x^2) diff(f(x),x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, a x \cos\left(a x^{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, a x \cos\left(a x^{2}\right)
#3) f(x)=cos(x)^3 diff(f(x),x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-3 \, \sin\left(x\right) \cos\left(x\right)^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}-3 \, \sin\left(x\right) \cos\left(x\right)^{2}
#5) f(x)=sec(a*x) diff(f(x),x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}a \tan\left(a x\right) \sec\left(a x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}a \tan\left(a x\right) \sec\left(a x\right)
#7) f(x)=cos(3*a*x) diff(f(x),x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-3 \, a \sin\left(3 \, a x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-3 \, a \sin\left(3 \, a x\right)
#9) var('y') f(y)=sin(2*y)*cos(y) diff(f(y),y) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(2 \, y\right) \sin\left(y\right) + 2 \, \cos\left(2 \, y\right) \cos\left(y\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(2 \, y\right) \sin\left(y\right) + 2 \, \cos\left(2 \, y\right) \cos\left(y\right)
#11) var('theta') f(theta)=tan(theta)-theta diff(f(theta),theta) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\tan\left(\theta\right)^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}\tan\left(\theta\right)^{2}
#13) var('t') f(t)=sin(t)^3*cos(t) show(f(t)) show(diff(f(t),t)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(t\right)^{3} \cos\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(t\right)^{4} + 3 \, \sin\left(t\right)^{2} \cos\left(t\right)^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(t\right)^{3} \cos\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(t\right)^{4} + 3 \, \sin\left(t\right)^{2} \cos\left(t\right)^{2}
#15) f(x)=sin(x)^2 show(f(x)) diff(f(x),x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(x\right)^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sin\left(x\right) \cos\left(x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(x\right)^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sin\left(x\right) \cos\left(x\right)