Learning Guide Learning Guide

5.3 Structural Manipulations • 185DE := −sin(t z(t)) sin(y(t)) cos(t) ( d dt y(t))− sin(t z(t)) sin(y(t)) cos(t)− sin(t z(t)) cos(y(t)) sin(t) ( d dt y(t))− sin(t z(t)) cos(y(t)) sin(t) + cos(t z(t)) cos(y(t)) cos(t) z(t)+ cos(t z(t)) cos(y(t)) cos(t) t ( d dt z(t))− cos(t z(t)) sin(y(t)) sin(t) z(t)− cos(t z(t)) sin(y(t)) sin(t) t ( d dt z(t)) + ( d dt x(t))> indets( DE, specfunc(anything, diff) );{ d dt y(t), ddt x(t), ddt z(t)}The following operands of DE contain the derivatives.> select( hastype, DE, specfunc(anything, diff) );−sin(t z(t)) sin(y(t)) cos(t) ( d dt y(t))− sin(t z(t)) cos(y(t)) sin(t) ( d dt y(t))+ cos(t z(t)) cos(y(t)) cos(t) t ( d dt z(t))− cos(t z(t)) sin(y(t)) sin(t) t ( d dt z(t)) + ( d dt x(t))DE has only one operand that is itself a derivative.> select( type, DE, specfunc(anything, diff) );ddt x(t)Maple recognizes many types. For a partial list, refer to ?type andfor more information on structured types, such as specfunc, refer to?type,structured.SubstitutionOften you want to substitute a value for a variable (that is, evaluate anexpression at a point). For example, if you need to solve the problem, “Iff(x) = ln(sin(xe cos(x) )), find f ′ (2),” then you must substitute the value 2for x in the derivative. The command finds the derivative.