SymPy - Derivative
The derivative of a function is its instantaneous rate of change with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.we can find the differentiation of mathematical expressions in the form of variables by using diff() function in SymPy package.
diff(expr, variable)
>>> from sympy import diff, sin, exp
>>> from sympy.abc import x,y
>>> expr=x*sin(x*x)+1 >>> expr
The above code snippet gives an output equivalent to the below expression −
$x\sin(x^2) + 1$
>>> diff(expr,x)
The above code snippet gives an output equivalent to the below expression −
$2x^2\cos(x^2) + \sin(x^2)$
>>> diff(exp(x**2),x)
The above code snippet gives an output equivalent to the below expression −
2xex2
To take multiple derivatives, pass the variable as many times as you wish to differentiate, or pass a number after the variable.
>>> diff(x**4,x,3)
The above code snippet gives an output equivalent to the below expression −
$24x$
>>> for i in range(1,4): print (diff(x**4,x,i))
The above code snippet gives the below expression −
4*x**3
12*x**2
24*x
It is also possible to call diff() method of an expression. It works similarly as diff() function.
>>> expr=x*sin(x*x)+1
>>> expr.diff(x)
The above code snippet gives an output equivalent to the below expression −
$2x^2\cos(x^2) + \sin(x^2)$
An unevaluated derivative is created by using the Derivative class. It has the same syntax as diff() function. To evaluate an unevaluated derivative, use the doit method.
>>> from sympy import Derivative
>>> d=Derivative(expr)
>>> d
The above code snippet gives an output equivalent to the below expression −
$\frac{d}{dx}(x\sin(x^2)+1)$
>>> d.doit()
The above code snippet gives an output equivalent to the below expression −
$2x^2\cos(x^2) + \sin(x^2)$
