Question

Dy/dx y = 3root(4x+1) -2x

Answer 1

Explanation:

`y=3*√(4x+1) -2x\\\\y'=(dy)/(dx) =(3)/(2*√(4x+1) ) -2\\\\\\\int {(3*√(4x+1) -2x}) \, dx \\\\=(3)/(4) *\int {4*(4x+1)}^{(1)/(2)} \, dx -2\int {x} \, dx \\\\=(-3)/(4)*√((4x+1)^3) *(2)/(3) }-x^2+C\\\\=(√((4x+1)^3))/(2) -x^2+C`

Answer 2

Explanation:

y = 3(4x + 1)^1/2 - 2x

dy/dx = 3*1/2(4x + 1)^-1/2 * 4 - 2

= 4 * 1.5 (4x + 1)^-1/2 - 2

= 6(4x + 1)^-1/2 - 2

= [6/√(4x + 1)] - 2

y = 3(4x + 1)^1/2 - 2x

∫3(4x + 1)^1/2 - 2x . dx

= 3 * 1/4 * (4x + 1)^3/2 / 3/2 - x^2 + C

= 3/4 * 2/3 (4x + 1)^3/2 - x^2 + C

= 1/2((4x + 1)^3/2 - 2x^2) + C.