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
RO
Related Maths A Level answers
All answers ▸If y=3x^3e^x; find dy/dx?
A stationary point of inflection implies a second derivative of 0, does this work the other way around?
When dealing with trigonometric functions such as sin, cos or tan, how do you solve the trigonometric equation when the argument of the function(s) is nx, where n is a real number not equal to 1.
curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.