parametric derivative test

1757 days ago by bardg

ecks(t) = cos(t)^7 
       
y(t) = sin(t)^2 
       
dydt = diff( y(t), t) 
       
dydt 
       
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sin\left(t\right) \cos\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sin\left(t\right) \cos\left(t\right)
dxdt = diff( ecks(t), t) 
       
dxdt 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-7 \, \sin\left(t\right) \cos\left(t\right)^{6}
\newcommand{\Bold}[1]{\mathbf{#1}}-7 \, \sin\left(t\right) \cos\left(t\right)^{6}
dydx = dydt/dxdt 
       
dydx 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2}{7 \, \cos\left(t\right)^{5}}
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2}{7 \, \cos\left(t\right)^{5}}
ddydxdt = diff( dydx, t ) 
       
ddydxdt 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{10 \, \sin\left(t\right)}{7 \, \cos\left(t\right)^{6}}
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{10 \, \sin\left(t\right)}{7 \, \cos\left(t\right)^{6}}
ddydxdx = ddydxdt / dxdt 
       
ddydxdx 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{10}{49 \, \cos\left(t\right)^{12}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{10}{49 \, \cos\left(t\right)^{12}}