when given 2 functions of x multipled by each other (as in 1e), the rule to use is product rule. do NOT memorise the formula blindly though. what i do is chant the steps.

for 1e, it goes differentiate one, keep the other PLUS differentiate the other one and keep this one. another tip for simplification (especially for equations with squareroots) is to factorise out the factor of lower power, which is the (4x^2 - 3)^-0.5 in this case.

for 1f, it goes square the bottom, keep the bottom and differentiate the top MINUS keep the top differentiate the bottom. it ensures my differentiation is consistent and systematic. alternatively, you can also convert the denominator to be part of the numerator (i.e (3x+1)^-1) and carry out product rule as per normal.