The chain rule · 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

The chain rule — objective 1

Maths4U Original · Short practice

Let \(f(x)=5 \left(3 x + 5\right)^{3}\), with real x.

Find f′(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

The chain rule — objective 1

Maths4U Original · Short practice

Let \(f(x)=2 \left(4 x + 1\right)^{4}\), with real x.

Find f′(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

The chain rule — objective 2

Maths4U Original · Short practice

Let \(f(x)=2 \left(4 x + 1\right)^{4}\), with real x.

Find f″(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

The chain rule — objective 2

Maths4U Original · Short practice

Let \(f(x)=3 \left(2 x + 2\right)^{2}\), with real x.

Find f″(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

The chain rule — objective 3

Maths4U Original · Short practice

Let \(f(x)=3 \left(2 x + 2\right)^{2}\), with real x.

Find f(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

The chain rule — objective 3

Maths4U Original · Short practice

Let \(f(x)=4 \left(3 x + 3\right)^{3}\), with real x.

Find f(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

The chain rule — objective 4

Maths4U Original · Short practice

Let \(f(x)=4 \left(3 x + 3\right)^{3}\), with real x.

Find the leading coefficient of f′(x).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

The chain rule — objective 4

Maths4U Original · Short practice

Let \(f(x)=5 \left(4 x + 4\right)^{4}\), with real x.

Find the leading coefficient of f′(x).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →