a. \(y'=x^2+4x-1\)
b. \(y'=-4x^3+4x\)
c. \(y'=\dfrac{\left(2x+3\right)\left(x-2\right)-\left(x^2+3x-1\right)}{\left(x-2\right)^2}=\dfrac{x^2-4x-5}{\left(x-2\right)^2}\)
d. \(y'=\dfrac{-\left(2x+3\right)-2\left(-x+1\right)}{\left(2x+3\right)^2}=\dfrac{-5}{\left(2x+3\right)^2}\)
e. \(y'=\dfrac{\left(x^2+3\right)'}{2\sqrt{x^2+3}}=\dfrac{x}{\sqrt{x^2+3}}\)
f. \(y'=6cos3x+2tanx.\left(tanx\right)'=6cos3x+\dfrac{2tanx}{cos^2x}\)