In[38]:= f@xD == 7 x^4 – 8 x^3 – x^2 + 78 Out[38]= f@xD 78 – x2 – 8 x3 + 7 x4 In[39]:= f’ == D@7 x^4 – 8 x^3 – x^2 + 78, xD Out[39]= f¢ -2 x – 24 x2 + 28 x3 In[46]:= h@xD == H2 – 5 xL H1 – x + x^2L Out[46]= h@xD 2 – 5 x 1 – x + x2 In[47]:= h’ == D@H2 – 5 xL H1 – x + x^2L, xD Out[47]= h¢ – H2 – 5 xL H-1 + 2 xL I1 – x + x2M2 – 5 1 – x + x2 The smplfied answer : In[48]:= h’ == Simplify@D@H2 – 5 xL H1 – x + x^2L, xDD Out[48]= h¢ -3 – 4 x + 5 x2 I1 – x + x2M2 In[49]:= f@xD == Sqrt@5 x^2 – 6 x + 1D Out[49]= f@xD 1 – 6 x + 5 x2 In[50]:= f’ == D@Sqrt@5 x^2 – 6 x + 1D, xD Out[50]= f¢ -6 + 10 x 2 1 – 6 x + 5 x2 In[51]:= h@xD == x^3 + x^H-4L + 2 Out[51]= h@xD 2 + 1 x4 + x3 In[52]:= h’ == D@x^3 + x^H-4L + 2, xD Out[52]= h¢ – 4 x5 + 3 x2 In[53]:= f@xD == e^Hx^2 – 3 x + 1L Out[53]= f@xD e1-3 x+x2 In[54]:= f’ == D@e^Hx^2 – 3 x + 1L, xD Out[54]= f¢ e1-3 x+x2 H-3 + 2 xL Log@eD
In[55]:= h@xD == x^H2 3L Out[55]= h@xD x23 In[56]:= h’ == D@x^H2 3L, xD Out[56]= h¢ 2 3 x13 In[57]:= f@xD == x^2 + x^H2 3L Out[57]= f@xD x23 + x2 In[58]:= f’ == D@x^2 + x^H2 3L, xD Out[58]= f¢ 2 3 x13 + 2 x In[59]:= h@xD = AtcTan@6 xD Out[59]= AtcTan@6 xD In[60]:= h’ == D@ArcTan@6 xD, xD Out[60]= h¢ 6 1 + 36 x2 In[61]:= f@xD == ArcTan@5 x + 4D Out[61]= f@xD ArcTan@4 + 5 xD In[62]:= f’ == D@ArcTan@5 x + 4D, xD Out[62]= f¢ 5 1 + H4 + 5 xL2 In[63]:= h@xD == ArcSin@2 x + 3D Out[63]= AtcTan@6 xD ArcSin@3 + 2 xD In[64]:= h’ == D@ArcSin@2 x + 3D, xD Out[64]= h¢ 2 1 – H3 + 2 xL2 In[65]:= f@xD == ArcSin@e^x + 1D Out[65]= f@xD ArcSin@1 + exD In[66]:= f’ == D@ArcSin@e^x + 1D, xD Out[66]= f¢ ex Log@eD 1 – H1 + exL2 2 Untitled-1