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1.10.2 Differentiating standard functions

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Question 1

Use the derivatives of sin⁡(x)\sin(x)sin(x) and cos⁡(x)\cos(x)cos(x) to show that:

a.
ddx(tan⁡x)=sec⁡2x \frac{d}{dx}(\tan x) = \sec^2 x dxd​(tanx)=sec2x
[3]
b.
ddx(sec⁡x)=sec⁡xtan⁡x \frac{d}{dx}(\sec x) = \sec x \tan x dxd​(secx)=secxtanx
[3]
c.
ddx(cot⁡x)=−csc⁡2x \frac{d}{dx}(\cot x) = -\csc^2 x dxd​(cotx)=−csc2x
[3]
d.
ddx(csc⁡x)=−csc⁡xcot⁡x \frac{d}{dx}(\csc x) = -\csc x \cot x dxd​(cscx)=−cscxcotx
[3]

1.10.2 Differentiating standard functions Questions

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