Logarithmic derivatives · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Logarithmic derivatives — objective 1

Maths4U Original · Short practice

Let \(f(x)=3 \log{\left(3 x + 3 \right)}\), with \(x>-1\).

Find f′(0).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Logarithmic derivatives — objective 1

Maths4U Original · Short practice

Let \(f(x)=4 \log{\left(x + 4 \right)}\), with \(x>-4\).

Find f′(0).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Method

Logarithmic derivatives — objective 2

Maths4U Original · Short practice

Let \(f(x)=4 \log{\left(x + 4 \right)}\), with \(x>-4\).

Find f″(0).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Logarithmic derivatives — objective 2

Maths4U Original · Short practice

Let \(f(x)=5 \log{\left(2 x + 5 \right)}\), with \(\displaystyle x>- \frac{5}{2}\).

Find f″(0).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Apply

Logarithmic derivatives — objective 3

Maths4U Original · Short practice

Let \(f(x)=5 \log{\left(2 x + 5 \right)}\), with \(\displaystyle x>- \frac{5}{2}\).

Find the x-coordinate of the vertical asymptote.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Logarithmic derivatives — objective 3

Maths4U Original · Short practice

Let \(f(x)=2 \log{\left(3 x + 1 \right)}\), with \(\displaystyle x>- \frac{1}{3}\).

Find the x-coordinate of the vertical asymptote.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Check understanding

Logarithmic derivatives — objective 4

Maths4U Original · Short practice

Let \(f(x)=2 \log{\left(3 x + 1 \right)}\), with \(\displaystyle x>- \frac{1}{3}\).

Find the gradient where the logarithm argument equals one.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Logarithmic derivatives — objective 4

Maths4U Original · Short practice

Let \(f(x)=3 \log{\left(x + 2 \right)}\), with \(x>-2\).

Find the gradient where the logarithm argument equals one.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Try written exam-style problems →