Before the midterm

Stopping at f′/f after logarithmic differentiation

The habit: The derivative of log f is f′/f, so multiply by f at the end.

7 practice questions are built to catch it, in 1 topic.

Practise against it: 6 questions

What it looks like

A question from the chain rule and logarithms, with the answer this slip gives beside the right one.

Standard3 marks · 5 min

Use logarithmic differentiation to find $f'(2)$ for the function below.

f(x) = \frac{x^{3}(x - 1)^{2}}{x + 1}

With the slip: $\displaystyle \approx 3.167$
Worked through: $\displaystyle f'(2) = \frac{76}{9}$

19/6 is f′(2)/f(2), the derivative of log f. Multiply by f(2) to finish.

See the worked solution

Where it comes up

The chain rule and logarithms7 questions

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

01
Use logarithmic differentiation to find $f'(1)$ for the function below. $\displaystyle f(x) = \frac{x^{2}\sqrt{x + 3}}{(x + 2)^{3}}$
The chain rule and logarithmsStandard
02
Let $f(x) = x^{4}(x - 2)^{3}(2x - 1)^{2}\left(x^{2} + 1\right)$ . Find $f'(1)$ .
The chain rule and logarithmsStandard
03
Let $f(x) = x^{\cos x}$ for $x > 0$ . Find $f'\!\left(\dfrac{\pi}{3}\right)$ .
The chain rule and logarithmsChallenging
04
Let $f(x) = (2 + \cos x)^{x}$ . Find $f'\!\left(\dfrac{\pi}{2}\right)$ .
The chain rule and logarithmsChallenging
05
Let $f(x) = x^{\sin x}$ for $x > 0$ . Use logarithmic differentiation to find $f'(x)$ .
The chain rule and logarithmsChallenging
06
Let $f$ be a differentiable function with $f(x) > 0$ for every $x$ , $f(1) = e$ and $f'(1) = 3$ . Let $g$ be the function below. Find $g'(1)$ . $\displaystyle g(x) = \bigl(f(x^{2})\bigr)^{x}$
The chain rule and logarithmsCapstone