Implicit differentiation and tangents · Short practice

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Recall

Implicit differentiation — objective 1

Maths4U Original · Short practice

The curve satisfies \(x^2+3xy+y^2=20\). Consider \(\displaystyle P=\)\(\left( 2, \ 2\right)\). For the short checks \(\displaystyle a=3\).

Find \(\displaystyle \frac{dy}{dx}\) at the stated point.

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

Implicit differentiation — objective 1

Maths4U Original · Short practice

The curve satisfies \(x^2+3xy+y^2=76\). Consider \(\displaystyle P=\)\(\left( 6, \ 2\right)\). For the short checks \(\displaystyle a=3\).

Find \(\displaystyle \frac{dy}{dx}\) at the stated point.

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

Implicit differentiation — objective 2

Maths4U Original · Short practice

The curve satisfies \(x^2+1xy+y^2=27\). Consider \(\displaystyle P=\)\(\left( 3, \ 3\right)\). For the short checks \(\displaystyle a=1\).

Find the tangent y-intercept there.

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

Implicit differentiation — objective 2

Maths4U Original · Short practice

The curve satisfies \(x^2+3xy+y^2=80\). Consider \(\displaystyle P=\)\(\left( 4, \ 4\right)\). For the short checks \(\displaystyle a=3\).

Find the tangent y-intercept there.

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

Implicit differentiation — objective 3

Maths4U Original · Short practice

The curve satisfies \(x^2+3xy+y^2=80\). Consider \(\displaystyle P=\)\(\left( 4, \ 4\right)\). For the short checks \(\displaystyle a=3\).

Find the normal gradient there.

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

Implicit differentiation — objective 3

Maths4U Original · Short practice

The curve satisfies \(x^2+3xy+y^2=76\). Consider \(\displaystyle P=\)\(\left( 6, \ 2\right)\). For the short checks \(\displaystyle a=3\).

Find the normal gradient there.

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

Implicit differentiation — objective 4

Maths4U Original · Short practice

The curve satisfies \(x^2+1xy+y^2=75\). Consider \(\displaystyle P=\)\(\left( 5, \ 5\right)\). For the short checks \(\displaystyle a=1\).

Find the value of \(\displaystyle x^{2}\)+axy+\(\displaystyle y^{2}\) at the stated point.

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

Implicit differentiation — objective 4

Maths4U Original · Short practice

The curve satisfies \(x^2+3xy+y^2=76\). Consider \(\displaystyle P=\)\(\left( 6, \ 2\right)\). For the short checks \(\displaystyle a=3\).

Find the value of \(\displaystyle x^{2}\)+axy+\(\displaystyle y^{2}\) at the stated point.

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.

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