Math 149 Quiz on differention key11 January 2012In[59]:=?DD@ f , xDgives the partial derivative ∑ f ê ∑ x.D@ f , 8x, n<D gives the multiple derivative ∑nf ê ∑ xn.D@ f , x, y, …D differentiates f successively with respect to x, y,….D@ f , 88x1, x2, …<<D for a scalar f gives the vector derivative H∑ fê∑ x1, ∑ fê∑ x2,…L.D@ f , 8array<D gives a tensor derivative. àPress and hold the “Shift” key, and then press the “Enter” key (while still holding down the “Shift” key after entering a Mathemat-ica command.1.In[60]:=D@13x^3 − 8x^2+ 5x − 3, xDOut[60]=5 − 16 x + 39 x2Assign a value to a variable, after clearing the variable, then differentiate:In[61]:=Clear@yDIn[62]:=y = 13x^3 − 8 x^2 + 5x − 3Out[62]=− 3 + 5x− 8x2+ 13 x3In[63]:=D@y, xDOut[63]=5 − 16 x + 39 x22.Define a function and display it:In[64]:=Clear@fDIn[65]:=f@x_D := Hax + bLêHcx + d LIn[66]:=f@xDOut[66]=b + axd + cxDifferentiate:In[67]:=D@f@xD,xDOut[67]=−c Hb + axLHd + cxL2+ad + cxIn[68]:=Together@%DOut[68]=− bc+ adHd + cxL2In[69]:=f'@xDOut[69]=−c Hb + axLHd + cxL2+ad + cxIn[70]:=Together@f'@xDDOut[70]=− bc+ adHd + cxL23.In[71]:=Clear@sDIn[72]:=s = H2 ê 3L u Sqrt@uDOut[72]=2u3ê23In[73]:=D@s, uDOut[73]=u4.In[74]:=Clear@wDIn[75]:=w = H6t + 2t^3L Cos@tDOut[75]=I6t+ 2t3M Cos@tDIn[76]:=D@w, tDOut[76]=I6 + 6t2M Cos@tD − I6t+ 2t3M [email protected][77]:=Clear@fDIn[78]:=f@T_D := H1 êH2LLL Sqrt@T ê RhoD2 Quiz00S12math.nbIn[79]:=f@TDOut[79]=TRho2LIn[80]:=f'@TDOut[80]=14 L RhoTRhoQuiz00S12math.nb
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