| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Differentiate exponential functions |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question testing standard rules (chain rule for exponentials and powers, plus basic logarithm differentiation). Both parts are routine applications with no problem-solving required, making it easier than average but not trivial since it requires correct application of multiple differentiation rules. |
| Spec | 1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{dy}{dx} = 3e^{3x} + \frac{1}{x}\) | B1M1A1 (3) | B1: \(3e^{3x}\); M1: \(\frac{a}{bx}\); A1: \(3e^{3x} + \frac{1}{x}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \((5+x^2)^{\frac{1}{2}}\) | B1 | |
| \(\frac{3}{2}(5+x^2)^{\frac{1}{2}} \cdot 2x = 3x(5+x^2)^{\frac{1}{2}}\) | M1A1 (3) | M1 for \(kx(5+x^2)^m\) |
# Question 2:
## Part (a)
$\frac{dy}{dx} = 3e^{3x} + \frac{1}{x}$ | B1M1A1 (3) | B1: $3e^{3x}$; M1: $\frac{a}{bx}$; A1: $3e^{3x} + \frac{1}{x}$
## Part (b)
$(5+x^2)^{\frac{1}{2}}$ | B1 |
$\frac{3}{2}(5+x^2)^{\frac{1}{2}} \cdot 2x = 3x(5+x^2)^{\frac{1}{2}}$ | M1A1 (3) | M1 for $kx(5+x^2)^m$
---Differentiate, with respect to $x$,
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { e } ^ { 3 x } + \ln 2 x$,
\item $\left( 5 + x ^ { 2 } \right) ^ { \frac { 3 } { 2 } }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 2006 Q2 [6]}}