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Scoped to Chain rule

34 matching questions

Chain rule

Practice · 34 questions

  1. Identifying the inside function

    For the function y=(4x+3)6y=(4x+3)^6, which expression is the inside function?
    Question 11 markMultiple-choiceNot attempted
    Open question

  2. Identifying the inside function in a quadratic composite

    For the function y=(2x2−5)4y=(2x^2-5)^4, which expression should be treated as the inside function when using the chain rule?
    Question 21 markMultiple-choiceNot attempted
    Open question

  3. Basic chain rule with (ax+b)n(ax+b)^n

    Differentiate y=(3x+2)5y=(3x+2)^5 with respect to xx.
    Question 32 marksAlgebraicNot attempted
    Open question

  4. Basic chain rule with (ax−b)n(ax-b)^n

    Differentiate y=(5x−4)3y=(5x-4)^3 with respect to xx.
    Question 42 marksAlgebraicNot attempted
    Open question

  5. Chain rule with a constant multiplier

    Differentiate y=2(4x+1)6y=2(4x+1)^6 with respect to xx.
    Question 52 marksAlgebraicNot attempted
    Open question

  6. Chain rule with quadratic inside functions

    Differentiate y=(x2+4)5y=(x^2+4)^5 with respect to xx.
    Question 62 marksAlgebraicNot attempted
    Open question

  7. Chain rule with quadratic inside functions

    Differentiate y=(3x2−2)4y=(3x^2-2)^4 with respect to xx.
    Question 72 marksAlgebraicNot attempted
    Open question

  8. Chain rule with fractional powers

    Differentiate y=(2x+7)1/2y=(2x+7)^{1/2} with respect to xx.
    Question 82 marksAlgebraicNot attempted
    Open question

  9. Chain rule with negative powers

    Differentiate y=(x2+1)−3y=(x^2+1)^{-3} with respect to xx.
    Question 92 marksAlgebraicNot attempted
    Open question

  10. Recognising when the chain rule is useful

    Which of the following functions are most naturally differentiated using the chain rule?
    Question 101 markMultiple-choiceNot attempted
    Open question

  11. Gradient at a point using chain rule

    For y=(2x+3)4y=(2x+3)^4, calculate the gradient of the curve at the point where x=1x=1.
    Question 113 marksNumericalNot attempted
    Open question

  12. Chain rule with a two-term inside derivative

    Differentiate y=(x2+4x)5y=(x^2+4x)^5 with respect to xx.
    Question 123 marksAlgebraicNot attempted
    Open question

  13. Gradient at a point with a constant multiplier

    For y=3(2x2−1)3y=3(2x^2-1)^3, calculate the value of dydx\frac{dy}{dx} when x=2x=2.
    Question 133 marksNumericalNot attempted
    Open question

  14. Chain rule with negative powers and positive-power final form

    Differentiate y=(3x−2)−4y=(3x-2)^{-4} with respect to xx, giving your answer with positive powers.
    Question 143 marksAlgebraicNot attempted
    Open question

  15. Gradient at a point with square-root chain rule

    For y=5x+4y=\sqrt{5x+4}, calculate dydx\frac{dy}{dx} when x=1x=1.
    Question 153 marksNumericalNot attempted
    Open question

  16. Rewrite square root then apply chain rule

    Differentiate y=7x−3y=\sqrt{7x-3} with respect to xx.
    Question 163 marksAlgebraicNot attempted
    Open question

  17. Rewrite reciprocal then apply chain rule

    Differentiate y=1(4x+5)3y=\frac{1}{(4x+5)^3} with respect to xx.
    Question 173 marksAlgebraicNot attempted
    Open question

  18. Gradient at a point using a quadratic inside function

    For y=(x2−2x+6)3y=(x^2-2x+6)^3, calculate the gradient of the curve at the point where x=2x=2.
    Question 183 marksNumericalNot attempted
    Open question

  19. Solving from a gradient condition

    For y=(2x+1)3y=(2x+1)^3, determine the positive value of xx for which the gradient of the curve is 54.
    Question 194 marksNumericalNot attempted
    Open question

  20. Chain rule with a negative bracket derivative

    Differentiate y=(7−2x)4y=(7-2x)^4 with respect to xx.
    Question 202 marksAlgebraicNot attempted
    Open question

  21. Chain rule with a negative linear bracket

    Differentiate y=(5−3x)5y=(5-3x)^5 with respect to xx.
    Question 213 marksAlgebraicNot attempted
    Open question

  22. Chain rule with a quadratic expression inside the bracket

    Differentiate y=(x2+3x+1)4y=(x^2+3x+1)^4 with respect to xx.
    Question 223 marksAlgebraicNot attempted
    Open question

  23. Chain rule with a negative quadratic inside function

    Differentiate y=(6−x2)5y=(6-x^2)^5 with respect to xx.
    Question 233 marksAlgebraicNot attempted
    Open question

  24. Chain rule with a constant multiplier and quadratic inside function

    Differentiate y=2(x2−1)5y=2(x^2-1)^5 with respect to xx.
    Question 243 marksAlgebraicNot attempted
    Open question
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