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 = 3x3-1 + (41)*x1-1 = 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.
