Chain Rule (Leaving Cert Mathematics): Quizzes

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Trigonometric Functions
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What is ddx[sin⁡(x)]\frac{d}{dx}[\sin(x)]?

cos⁡(x)\cos(x)

What is ddx[cos⁡(x)]\frac{d}{dx}[\cos(x)]?

−sin⁡(x)-\sin(x)

What is ddx[tan⁡(x)]\frac{d}{dx}[\tan(x)]?

sec⁡2(x)\sec^2(x)

Which rule is needed to differentiate sin⁡(g(x))\sin(g(x)) where g(x)g(x) is a function of xx?

Chain rule

What is the derivative of cos⁡(7x−3)\cos(7x-3)?

−7sin⁡(7x−3)-7\sin(7x-3)

When differentiating cos⁡(7x−3)\cos(7x-3), what is the inner function vv?

7x−37x-3

How is sin⁡2(x)\sin^2(x) rewritten using general notation?

(sin⁡(x))2(\sin(x))^2

What is the derivative of sin⁡(5x+2)\sin(5x+2)?

5cos⁡(5x+2)5\cos(5x+2)

What is the derivative of sin⁡2(5x+2)\sin^2(5x+2)?

10sin⁡(5x+2)cos⁡(5x+2)10\sin(5x+2)\cos(5x+2)

Where can the derivatives of basic trigonometric functions be found?

In the log tables

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