What is the gradient of this curve y=5x^3+6x^2+7x+8 at point x=3?

When differentiating an equation (y) you find the equation of the gradient, called dy/dx. The rule for differentiating a power of x is given below:y=x^n dy/dx= nx^(n-1)Applying this rule to this question you get dy/dx=15x^2+12x+7, this is the equation of the gradient. To find the gradient at x=3, substitute x=3 into dy/dx. This gives the gradient (dy/dx) as 178.