5 months ago
Q:

Solve the following derivatives using rules and derivative algebra (give the simplified result). f(x)= (4x - 1)/(2x^2+3x-1)

Accepted Solution

A:
$\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 4x-1 \right) \times \left( 2{x}^{2}+3x-1 \right)-\left( 4x-1 \right) \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{x}^{2}+3x-1 \right) }{ {\left( 2{x}^{2}+3x-1 \right)}^{2} }$
$\frac{ 4\left( 2{x}^{2}+3x-1 \right)-\left( 4x-1 \right) \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{x}^{2}+3x-1 \right) }{ {\left( 2{x}^{2}+3x-1 \right)}^{2} }$
$\frac{ 4\left( 2{x}^{2}+3x-1 \right)-\left( 4x-1 \right) \times \left( 2 \times 2x+3 \right) }{ {\left( 2{x}^{2}+3x-1 \right)}^{2} }$
$\frac{ -8{x}^{2}+4x-1 }{ {\left( 2{x}^{2}+3x-1 \right)}^{2} }$