L3 Differentiation
Question Bank
If $mx + ny^2 = c$, where $m$, $n$ and $c$ are constants, find an expression for $\dfrac{dy}{dx}$ in terms of $m$, $n$ and $y$.
Find the gradient of the curve $x^2 + y^2 - 10x = 2y - 21$ at the point $(4, 3)$ on the curve.
You must use calculus and show any derivatives that you need to find when solving this problem.
Find $\dfrac{dy}{dx}$ if $2x^2y + 5y = 3x^2$.
The ellipse $4x^2 + 9y^2 = 72$ passes through the point $(3, 2)$.
Find the equation of the tangent to the ellipse at this point. Give your answer in the form $ax + by + c = 0$.
You must use calculus and show any derivatives that you need to find when solving this problem.
The curve $(y - 2)^2 = 8(x + 1)$ passes through the point $(7, -6)$.
Find the gradient of the curve at this point, and the equation of the tangent there in the form $ax + by + c = 0$.
You must use calculus and show any derivatives that you need to find when solving this problem.
Find the coordinates of the points on the curve $x^2 + xy + y^2 = 12$ where the tangent is horizontal.
You must use calculus and show any derivatives that you need to find when solving this problem.