Step-by-step explanation:
To find the derivative of
3x+5, apply sum rule
[tex] \frac{d}{dx}(3x + 5) = \frac{d}{dx} 3x + \frac{d}{dx} 5[/tex]
The derivative of
[tex] \frac{d}{dx} kx = k[/tex]
And
[tex] \frac{d}{dx} c = 0[/tex]
So we have
[tex] \frac{d}{dx} 3x + 5 = 3[/tex]
So the derivative of the function is 3,
Since linear equations have a constant slope, the slope at any point will be 3.
So the slope of the tangent line is 3.
