:"e4a1ddda-ef34-4475-bf42-8ac60d56a9b8","topicSlug":"differentiation-6","cards":[{"id":"8c79f25d-9331-4dac-9909-7498c85e2466","cardType":"basic","front":"What does the derivative give at a chosen point on a curve?","back":"The gradient, or instantaneous rate of change.","points":1,"mcqOptions":null},{"id":"8adfb67b-e5b6-42fa-bdec-58915bb67f78","cardType":"basic","front":"What does $f'(x)$ represent?","back":"The derivative of $f(x)$.","points":1,"mcqOptions":null},{"id":"a9028a9e-6e3c-40dd-baed-04432b0e38f4","cardType":"cloze","front":"$$\\frac{dy}{dx}$ is the [ ] of $y$ with respect to $x$.","back":"$$\\frac{dy}{dx}$ is the derivative of $y$ with respect to $x$.","points":null,"mcqOptions":null},{"id":"4daab08d-cce3-47ca-b09b-5e6071e8abe9","cardType":"cloze","front":"$$\\frac{dy}{dx}$ is the derivative of $y$ with respect to $\\text{[...]}$.","back":"$$\\frac{dy}{dx}$ is the derivative of $y$ with respect to $\\boxed{x}$.","points":null,"mcqOptions":null},{"id":"dc1e9e9e-b7fb-43f2-8426-4009dc853c78","cardType":"cloze","front":"To differentiate $x^n$, multiply by $\\text{[...]}$ and change the power to $n-1$.","back":"To differentiate $x^n$, multiply by $\\boxed{n}$ and change the power to $n-1$.","points":null,"mcqOptions":null},{"id":"a106e34d-0546-41be-aa0a-3034fdf3fd54","cardType":"cloze","front":"To differentiate $x^n$, multiply by $n$ and change the power to $\\text{[...]}$.","back":"To differentiate $x^n$, multiply by $n$ and change the power to $\\boxed{n-1}$.","points":null,"mcqOptions":null},{"id":"3c392f08-a8e6-474c-931e-ac1d10a7467f","cardType":"basic","front":"Why is the derivative of a constant zero?","back":"Its value does not change as $x$ changes.","points":2,"mcqOptions":null},{"id":"2f02900e-bcb1-4a8c-90ba-5bf621207b5a","cardType":"basic","front":"What happens to a constant multiplier when differentiating?","back":"It remains as a multiplier of the derivative.","points":1,"mcqOptions":null},{"id":"14ee58ae-361b-4f1f-859b-e06e15b523cb","cardType":"basic","front":"How are sums and differences differentiated?","back":"Differentiate each term separately, preserving its sign.","points":2,"mcqOptions":null},{"id":"db0ad7b5-0bfb-4cc5-a43f-34dca0d101da","cardType":"basic","front":"Rewrite $\\sqrt{x}$ as a power of $x$.","back":"$x^{\\frac12}$","points":1,"mcqOptions":null},{"id":"587727de-b060-4fe5-8d20-4467866976f4","cardType":"basic","front":"Rewrite $\\frac{1}{x}$ as a power of $x$.","back":"$x^{-1}$","points":1,"mcqOptions":null},{"id":"a9d5f6c4-e985-43bb-97fd-e68244bbefba","cardType":"basic","front":"Differentiate $x^5$.","back":"$5x^4$","points":1,"mcqOptions":null},{"id":"afa277bb-52d5-408d-87c1-fc1a63cfac27","cardType":"basic","front":"Differentiate $7x^4$.","back":"$28x^3$","points":1,"mcqOptions":null},{"id":"0e65249e-1d43-49f1-9daa-0e366d800061","cardType":"basic","front":"Differentiate $6x^3$.","back":"$18x^2$","points":1,"mcqOptions":null},{"id":"5f0e3d64-eeff-4c9f-b962-ce9d13a0edc9","cardType":"basic","front":"Differentiate $-\\frac{5}{2}x^6$.","back":"$-15x^5$","points":1,"mcqOptions":null},{"id":"fc9d86c2-1e1a-48d8-8099-ebdc1279ac40","cardType":"cloze","front":"For $ax^n$, the derivative has coefficient $\\text{[...]}$ and power $n-1$.","back":"For $ax^n$, the derivative has coefficient $\\boxed{an}$ and power $n-1$.","points":null,"mcqOptions":null},{"id":"536e25e4-d1dd-4d2a-864a-652e1f2368a9","cardType":"cloze","front":"For $ax^n$, the derivative has coefficient

1.6.5 Differentiation Flashcards

1.6.5 Differentiation Flashcards