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Basic differentiation
Foundations · 3 questions
- Question 11 markNot attemptedAlgebraic question
Differentiate a power
Differentiate f(x)=x^5 .
- Question 22 marksNot attemptedAlgebraic question
Differentiate a sum of powers
Differentiate y=3x^4-2x^2+7 .
- Question 32 marksNot attemptedNumerical question
Evaluate a derivative
For f(x)=x^3+2x , find f'(2) .
Basic differentiation
Applications · 3 questions
- Question 43 marksNot attemptedNumerical question
Find gradient at a point
The curve has equation y=2x^3-x^2 . Find the gradient of the curve when…
- Question 53 marksNot attemptedNumerical question
Tangent gradient
Find the gradient of the tangent to y=x^4-3x at x=2 .
- Question 63 marksNot attemptedNumerical question
Stationary point condition
For y=x^2-6x+4 , find the x -coordinate of the stationary point.
Basic differentiation
Past Paper-style Questions · 2 questions
- Question 73 marksNot attemptedNumerical question
Exam-style tangent problem
The curve y=x^3-4x+1 has a tangent at the point where x=2 . Find the…
- Question 84 marksNot attemptedNumerical question
Exam-style stationary point
A curve has equation y=x^3-12x+5 . Find the positive x -coordinate of a…
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 .
Future Higher Maths coverage
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Straight Lines · Circles · Sequences
Vector Connections · Vector Operations
Differentiation · Integration · Applying Calculus
Polynomials · Logarithms and Exponentials · Trigonometric Skills · Functions and Graphs · Intersections