Moderate -0.5 This is a straightforward application of the standard derivative formula d/dx(sin⁻¹x) = 1/√(1-x²), requiring only substitution of x=1/5 and simplification. Being multiple choice with 1 mark makes it easier than average, though it's from Further Maths so involves a less common derivative that students must recall correctly.
Find the gradient of the tangent to the curve
$$y = \sin^{-1} x$$
at the point where \(x = \frac{1}{5}\)
Circle your answer.
[1 mark]
\(\frac{5\sqrt{6}}{12}\) \quad \(\frac{2\sqrt{6}}{5}\) \quad \(\frac{4\sqrt{3}}{25}\) \quad \(\frac{25}{24}\)
Find the gradient of the tangent to the curve
$$y = \sin^{-1} x$$
at the point where $x = \frac{1}{5}$
Circle your answer.
[1 mark]
$\frac{5\sqrt{6}}{12}$ \quad $\frac{2\sqrt{6}}{5}$ \quad $\frac{4\sqrt{3}}{25}$ \quad $\frac{25}{24}$
\hfill \mbox{\textit{AQA Further Paper 2 2020 Q3 [1]}}