Differentiation and its applications quiz: O-Level Additional Mathematics (SEAB 4049) quiz

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

Differentiate $y = x^5$.

What is $\dfrac{d}{dx}(\sin x)$?

What is the derivative of $\ln x$?

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

Differentiate $y = x \cos x$ using the product rule.

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

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

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 $y$ and $x$ both vary with time, the chain rule gives $\dfrac{dy}{dt}$ as:

The radius of a circle increases at $2$ cm per second. Using $A = \pi r^2$, what is $\dfrac{dA}{dt}$ when $r = 5$ cm?

Differentiate $y = e^{2x}$.