Differentiation Practice Questions

State what $\dfrac{dy}{dx}$ tells you about the curve.

Work out $\dfrac{dy}{dx}$

Work out the gradient of the curve at the point where $x = 1$

$y = 5x^4 + \dfrac{3}{x}$

Work out $\dfrac{dy}{dx}$

Work out $\dfrac{dy}{dx}$

Work out the rate of change of $y$ with respect to $x$ when $x = 2$

$y = \dfrac{6x^5 - x^2}{2x^3}$

Work out $\dfrac{dy}{dx}$

$y = \dfrac{1}{3}x^3 - 2x + 1$

Work out the values of $x$ for which the rate of change of $y$ with respect to $x$ is $14$

Work out $\dfrac{d^2y}{dx^2}$

Work out the value of $\dfrac{d^2y}{dx^2}$ when $x = -1$

Complete the sentence.

$\dfrac{d^2y}{dx^2}$ measures the rate of change of ______________ with respect to $x$.

The equation of a curve is $y = 2x^3 - 9x^2 + 12x + 1$

Work out the values of $x$ for which the gradient of the curve is zero.

You must show your working.

The equation of a curve is $y = 2x^3 + kx^2 - 5x$, where $k$ is a constant.

When $x = 3$ the gradient of the curve is $43$

Work out the value of $k$.

The equation of a curve is $y = ax^3 + \dfrac{b}{x^2}$, where $a$ and $b$ are constants.

The curve passes through the point $(1, 5)$ and the gradient of the curve at this point is $5$

Work out the values of $a$ and $b$.

Show that $y = 4x + 4x^{-1} + x^{-3}$

Work out $\dfrac{d^2y}{dx^2}$