Question

Answer 1

1: y'=5x^4+3*4x^3-2x+3

=5x^4+12x^3-2x+3

2: y'=4x^3-3*3x^2-1/x^2

=4x^3-9x^2-1/x^2

3: \(y'=\left(\sqrt{x}\right)'\cdot\left(2x^2+1\right)+\left(2x^2+1\right)'\cdot\left(\sqrt{x}\right)\)

\(=\dfrac{1}{2\sqrt{x}}\cdot\left(2x^2+1\right)+4x\cdot\sqrt{x}\)

5: 

\(y'=\dfrac{\left(x+1\right)'\cdot\left(x-3\right)-\left(x-3\right)'\cdot\left(x+1\right)}{\left(x-3\right)^2}\)

\(=\dfrac{x-3-x-1}{\left(x-3\right)^2}=\dfrac{-4}{\left(x-3\right)^2}\)