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Instant-use add-on functions for the Wolfram Language
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Compute a partial derivative with respect to a complex variable or its conjugate
gives the partial derivative , where z is complex.
gives the partial derivative with respect to the complex conjugate of z.
gives the multiple derivative.
Complex derivative of a function:
ComplexD works with Abs:
Compare ComplexD with its definition for a function:
Find the complex derivative using the definition in terms of derivatives with respect to the real and imaginary parts:
Use ComplexExpand on the output of ComplexD:
More complicated expressions can be differentiated by first complex expanding the expression into one that consists of Conjugate only:
Use ComplexD to find the real derivative (i.e. the derivative with respect to the real part only):
For example, here is the "real" derivative of Abs:
Compare to the usual definition of the real derivative (h is treated as real here):
The complex variable z and its conjugate are independent:
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