Differentiating nonnegative integer powers · Short practice

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Recall

Differentiating nonnegative integer powers — objective 1

Maths4U Original · Short practice

\(f(x)=4 x^{5} - 5 x + 1\).

Find the coefficient of \(\displaystyle x^4\) in f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Differentiating nonnegative integer powers — objective 1

Maths4U Original · Short practice

\(f(x)=x^{3} - 6 x + 2\).

Find the coefficient of \(\displaystyle x^2\) in f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Method

Differentiating nonnegative integer powers — objective 2

Maths4U Original · Short practice

\(f(x)=x^{3} - 6 x + 2\).

Find the constant term of f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Differentiating nonnegative integer powers — objective 2

Maths4U Original · Short practice

\(f(x)=2 x^{4} - 7 x + 3\).

Find the constant term of f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Apply

Differentiating nonnegative integer powers — objective 3

Maths4U Original · Short practice

\(f(x)=2 x^{4} - 7 x + 3\).

Find the gradient at \(\displaystyle x=2\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Differentiating nonnegative integer powers — objective 3

Maths4U Original · Short practice

\(f(x)=3 x^{5} - 8 x + 4\).

Find the gradient at \(\displaystyle x=3\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Check understanding

Differentiating nonnegative integer powers — objective 4

Maths4U Original · Short practice

\(f(x)=3 x^{5} - 8 x + 4\).

Find f″(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Differentiating nonnegative integer powers — objective 4

Maths4U Original · Short practice

\(f(x)=4 x^{3} - 2 x - 4\).

Find f″(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Try written exam-style problems →