Given y = x^3 + 4x + 1, find the value of dy/dx when x=3

To differentiate this equation, you must bring the power of each x term down to the front and reduce the power of x by 1, with constants disappearing:

dy/dx = 3x^3-1 + (41)*x^1-1 =  3x² + 4

To find the value of this when x=3, simply substitute this value into the equation for dy/dx:

dy/dx = 3(3)² + 4 = 27 + 4 = 31

This value represents the gradient of the line y = x³+4x+1 when x=3.