Answer:
[tex]derivative \: of \: y = 6 {x}^{2} + 2x + 4[/tex]
Step-by-step explanation:
we know that
[tex] \frac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]
Now the derivative of y=2x³+x²+4x
[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} + {x}^{2} + 4x)[/tex]
[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} ) + \frac{d}{dx}( {x}^{2} ) + \frac{d}{dx} (4x)[/tex]
[tex]\frac{dy}{dx} = 2(\frac{d}{dx} {x}^{3} ) + \frac{d}{dx} {x}^{2} + 4(\frac{d}{dx} x)[/tex]
here
[tex]\frac{d}{dx} {x}^{3} = 3 {x}^{2} [/tex]
[tex]\frac{d}{dx} {x}^{2} = 2x[/tex]
[tex]\frac{d}{dx} x = 1[/tex]
Now
[tex]\frac{dy}{dx} = 2(3 {x}^{2} ) + 2x + 4(1)[/tex]
[tex]\frac{dy}{dx} = 6 {x}^{2} + 2x + 4[/tex]
I hope it helped you
