Let f(x) = 5x^4 + 6x^3 + 3, find dy/dx at x = 3

First we must differentiate the equation with respect to x. To differentiate you must multiply the coefficient (number in front) by the power of x, then subtract 1 from the power. So here we find dy/dx = (54)x^(4-1) + (63)x^(3-1) + (1*0) = 20x^3 + 18x^2.

To find the value of dy/dx at x=3 we must substitute x=3 into the equation we just found. This gives dy/dx = (203^3) + (183^2) = 540 + 162 = 702. This value is the gradient of the line at x=3.