3.5.4 Differentiation (A-level only)

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Question 42

The curve $C\,$ has equation

2\tan\left(y + \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{3\pi}{4} < y < \frac{\pi}{4}

a.

Show that

\frac{dy}{dx} = \frac{a}{x^2 + b}

where $a\,$ and $b\,$ are integers to be found.

[5]

b.

The point $P\,$ with $y$ -coordinate 0 lies on $C$ . The tangent to $C\,$ at $P\,$ crosses the $x$ -axis at the point $Q$ . Find the exact $x$ -coordinate of $Q$ .

[4]

3.5.4 Differentiation (A-level only)

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Question 42

The curve $C\,$ has equation

2\tan\left(y + \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{3\pi}{4} < y < \frac{\pi}{4}

a.

Show that

\frac{dy}{dx} = \frac{a}{x^2 + b}

where $a\,$ and $b\,$ are integers to be found.

[5]

b.

The point $P\,$ with $y$ -coordinate 0 lies on $C$ . The tangent to $C\,$ at $P\,$ crosses the $x$ -axis at the point $Q$ . Find the exact $x$ -coordinate of $Q$ .

[4]

3.5.4 Differentiation (A-level only)

Question 42

3.5.4 Differentiation (A-level only) Questions

3.5.4 Differentiation (A-level only)

Question 42

3.5.4 Differentiation (A-level only) Questions