MPe

def differentiate(fxn):
    if fxn == '(x)' or fxn == 'x':
        return '1'
    else:
        open = fxn.find('(')
        close = fxn.rfind(')')
        gxn = fxn[open:close+1]
        coefficient = fxn[:open]
        exponent = fxn[close+1:]
        trig = ''
        trigs = ['sin','cos','tan','csc','sec','cot']
        if coefficient == "":
            coefficient = 1
        elif coefficient == "-":
            coefficient = -1
        elif coefficient not in trigs:
            coefficient = int(coefficient)
        else:
            trig = coefficient
            coefficient = 1

        if exponent == '':
            exponent = 1
        else:
            exponent = int(exponent[1:])

        fdx = ''

        if trig == '':
            coefficient *= exponent
            exponent -= 1
            fdx = gxn
        else:
            if trig == 'sin':
                fdx = 'cos' + gxn
            elif trig == 'cos':
                fdx = 'sin' + gxn
                coefficient *= -1
            elif trig == 'tan':
                fdx = 'sec' + gxn
                exponent *= 2
            elif trig == 'csc':
                fdx = 'csc' + gxn + 'cot' + gxn
                coefficient *= -1
            elif trig == 'sec':
                fdx = 'sec' + gxn + 'tan' + gxn
            elif trig == 'cot':
                fdx = 'csc' + gxn
                exponent *= 2
                coefficient *= -1

        parentheses = exponent > 1 or coefficient < 0 or trig != ''

        if exponent == 1:
            exponent = ''
        else:
            exponent = '^{}'.format(str(exponent))

        if coefficient == 1:
            coefficient = ''
        elif coefficient == -1:
            coefficient = '-'
        else:
            coefficient = str(coefficient)

        if parentheses == True:
            coefficient = "({}".format(coefficient)
            exponent = "{})".format(exponent)

        gdx = differentiate(gxn[1:len(gxn)-1])

        if gdx == '1':
            gdx = ''
        else:
            gdx = "*{}".format(gdx)

        fdx = coefficient + fdx + exponent + gdx

        return fdx