D D[f, x] gives the partial derivative . D[f, {x, n}] gives the multiple derivative . D[f, , , ... ] gives . D can be used to find the rate of change of a function. D[f, x] can be input as . The character is entered as pd or \[PartialD]. The variable x is entered as a subscript. An alternative notation for taking the derivative of a function of one variable is f'[x] which is equivalent to D[f[x], x]. f''[x] denotes the second derivative of f with respect to x. All quantities that do not explicitly depend on the are taken to have zero partial derivative. The derivatives of built-in mathematical functions are evaluated when possible in terms of other built-in mathematical functions. D uses the chain rule to simplify derivatives of unknown functions. D[f, x, y] can be input as . The character \[InvisibleComma], entered as ,, can be used instead of an ordinary comma. It does not display but is still interpreted just like a comma. See also: Integrate, ND. Examples Using InstantCalculators Here are the InstantCalculators for the D function. Enter the parameters for your calculation and click Calculate to see the result. In[1]:= Out[1]= In[2]:= Out[2]= Entering Commands Directly You can paste a template for this command via the Text Input button on the D Function Controller. Here is the derivative of with respect to x. In[3]:= Out[3]= In[4]:= Out[4]= Here is the Chain Rule of first-year calculus. In[5]:= Out[5]= If you differentiate a function with respect to x, say, all other parameters are treated as constants. In[6]:= Out[6]= This gives the fourth derivative of with respect to x. In[7]:= Out[7]= Here is the partial derivative . In[8]:= Out[8]= Mathematical Input Notation This also gives the fourth derivative of with respect to x. In[9]:= Out[9]= This also gives the partial derivative . In[10]:= Out[10]=

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