Find the gradient of the tangent to the curve with the equation y = (3x^4 - 18)/x at the point where x = 3

y = (3x⁴ - 18)/x

The gradient of a tangent to a curve is equal to dy/dx 

However, we must simplify this equation before we can differentiate it;

y = 3x³ - 18/x = 3x³ - 18x^-1

dy/dx = 3(3x²) - (-1)(18x^-2)

= 9x² + 18x^-2 = 9x² + 18/x²

When x = 3,

dy/dx = 9(9) + 18/9 = 83