n Flashcards","topicId":"b5089a24-6528-4d61-a590-5663ae1f5237","topicSlug":"differentiate-y-kx-n","cards":[{"id":"c11406ee-c27a-4fb4-bf32-3da0564be539","cardType":"cloze","front":"For $y=kx^n$, the power rule gives $\\text{[...]}$.","back":"For $y=kx^n$, the power rule gives $\\boxed{\\dfrac{dy}{dx}=knx^{n-1}}$.","points":null,"mcqOptions":null},{"id":"52ffe3aa-2144-44fa-a2c2-191d8b5fab4f","cardType":"cloze","front":"Geometrically, the derivative gives the [ ] to a curve.","back":"Geometrically, the derivative gives the gradient of the tangent to a curve.","points":null,"mcqOptions":null},{"id":"e8cc692c-d5fa-44b8-890e-eccb65096d2e","cardType":"basic","front":"State three equivalent notations for a derivative.","back":"

$\\dfrac{dy}{dx}$
$y'$
$f'(x)$

","points":3,"mcqOptions":null},{"id":"cd9a3638-e1b8-43af-b2a5-2556b289ce24","cardType":"basic","front":"Why is the derivative of a constant zero?","back":"It does not change as $x$ changes.","points":2,"mcqOptions":null},{"id":"ee859a0c-7e81-4fc5-9041-28e01f54d9da","cardType":"basic","front":"Differentiate $y=kx$.","back":"$\\dfrac{dy}{dx}=k$","points":1,"mcqOptions":null},{"id":"2593afb6-abe5-487e-930c-9a3ac2b78c3a","cardType":"cloze","front":"The power rule for $kx^n$ applies when $n$ is any [ ].","back":"The power rule for $kx^n$ applies when $n$ is any rational number.","points":null,"mcqOptions":null},{"id":"082022d5-b628-454f-b867-bd18a464128c","cardType":"cloze","front":"A variable in a denominator is rewritten using a [ ] before differentiation.","back":"A variable in a denominator is rewritten using a negative power before differentiation.","points":null,"mcqOptions":null},{"id":"18d255bb-1f74-4914-a1a1-b3f45ebf1b10","cardType":"cloze","front":"In index form, $\\sqrt{x}=$ $\\text{[...]}$.","back":"In index form, $\\sqrt{x}=$ $\\boxed{x^{1/2}}$.","points":null,"mcqOptions":null},{"id":"5d30c6b1-e00e-4500-bb98-94da32e97a56","cardType":"basic","front":"Rewrite $\\dfrac{1}{\\sqrt{x}}$ in index form.","back":"$x^{-1/2}$","points":1,"mcqOptions":null},{"id":"4b721e68-fc9b-4d2e-829f-92ab630e9d69","cardType":"basic","front":"How are sums and differences differentiated?","back":"

Differentiate each term separately.
Retain the addition and subtraction signs.

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1.9.5 Differentiate y = kx^n Flashcards

1.9.5 Differentiate y = kx^n Flashcards