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Chain rule
Foundations · 10 questions
- Question 11 markNot attemptedMultiple-choice question
Identifying the inside function
For the function y=(4x+3)^6 , which expression is the inside function?…
- Question 21 markNot attemptedMultiple-choice question
Identifying the inside function in a quadratic composite
For the function y=(2x^2-5)^4 , which expression should be treated as…
- Question 32 marksNot attemptedAlgebraic question
Basic chain rule with $(ax+b)^n$
Differentiate y=(3x+2)^5 with respect to x .
- Question 42 marksNot attemptedAlgebraic question
Basic chain rule with $(ax-b)^n$
Differentiate y=(5x-4)^3 with respect to x .
- Question 52 marksNot attemptedAlgebraic question
Chain rule with a constant multiplier
Differentiate y=2(4x+1)^6 with respect to x .
- Question 62 marksNot attemptedAlgebraic question
Chain rule with quadratic inside functions
Differentiate y=(x^2+4)^5 with respect to x .
- Question 72 marksNot attemptedAlgebraic question
Chain rule with quadratic inside functions
Differentiate y=(3x^2-2)^4 with respect to x .
- Question 82 marksNot attemptedAlgebraic question
Chain rule with fractional powers
Differentiate y=(2x+7)^1/2 with respect to x .
- Question 92 marksNot attemptedAlgebraic question
Chain rule with negative powers
Differentiate y=(x^2+1)^-3 with respect to x .
- Question 101 markNot attemptedMultiple-choice question
Recognising when the chain rule is useful
Which of the following functions are most naturally differentiated…
Chain rule
Applications · 9 questions
- Question 113 marksNot attemptedNumerical question
Gradient at a point using chain rule
For y=(2x+3)^4 , calculate the gradient of the curve at the point where…
- Question 123 marksNot attemptedAlgebraic question
Chain rule with a two-term inside derivative
Differentiate y=(x^2+4x)^5 with respect to x .
- Question 133 marksNot attemptedNumerical question
Gradient at a point with a constant multiplier
For y=3(2x^2-1)^3 , calculate the value of dy/dx when x=2 .
- Question 143 marksNot attemptedAlgebraic question
Chain rule with negative powers and positive-power final form
Differentiate y=(3x-2)^-4 with respect to x , giving your answer with…
- Question 153 marksNot attemptedNumerical question
Gradient at a point with square-root chain rule
For y=sqrt(5x+4) , calculate dy/dx when x=1 .
- Question 163 marksNot attemptedAlgebraic question
Rewrite square root then apply chain rule
Differentiate y=sqrt(7x-3) with respect to x .
- Question 173 marksNot attemptedAlgebraic question
Rewrite reciprocal then apply chain rule
Differentiate y=1/(4x+5)^3 with respect to x .
- Question 183 marksNot attemptedNumerical question
Gradient at a point using a quadratic inside function
For y=(x^2-2x+6)^3 , calculate the gradient of the curve at the point…
- Question 194 marksNot attemptedNumerical question
Solving from a gradient condition
For y=(2x+1)^3 , determine the positive value of x for which the…
Chain rule
Past Paper-style Questions · 15 questions
- Question 202 marksNot attemptedAlgebraic question
Chain rule with a negative bracket derivative
Differentiate y=(7-2x)^4 with respect to x .
- Question 213 marksNot attemptedAlgebraic question
Chain rule with a negative linear bracket
Differentiate y=(5-3x)^5 with respect to x .
- Question 223 marksNot attemptedAlgebraic question
Chain rule with a quadratic expression inside the bracket
Differentiate y=(x^2+3x+1)^4 with respect to x .
- Question 233 marksNot attemptedAlgebraic question
Chain rule with a negative quadratic inside function
Differentiate y=(6-x^2)^5 with respect to x .
- Question 243 marksNot attemptedAlgebraic question
Chain rule with a constant multiplier and quadratic inside function
Differentiate y=2(x^2-1)^5 with respect to x .
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