Differentiation quiz: N(A)-Level Additional Mathematics (SEAB 4051) quiz

What does $\dfrac{dy}{dx}$ represent at a point on the curve $y = f(x)$?

Differentiate $y = x^5$.

Differentiate $y = 4x^3 - x$.

Which rule differentiates a composite function such as $(3x + 1)^4$?

Differentiate $y = (2x + 1)^3$.

Using the product rule, differentiate $y = x^2(x + 1)$ after first identifying $u$ and $v$.

The gradient of the normal to a curve, where the tangent gradient is $m$, is:

Find the tangent gradient to $y = x^2$ at $x = 3$.

Find the equation of the tangent to $y = x^2$ at the point $(1, 1)$.

At a stationary point, $\dfrac{dy}{dx}$ equals:

By the second derivative test, a stationary point where $\dfrac{d^2y}{dx^2} < 0$ is a:

Find the stationary point of $y = x^2 - 4x + 1$.

If the second derivative test gives $\dfrac{d^2y}{dx^2} = 0$ at a stationary point, you should:

Differentiate $y = \dfrac{1}{x}$ by first writing it as a power of $x$.