Differentiating Other Functions (Trig, ln & e etc) (Edexcel A-Level Mathematics): Flashcards

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Differentiating Other Functions (Trig, ln & e etc)
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What is the derivative of sin⁡(x)\sin(x)?

ddxsin⁡(x)=cos⁡(x)\frac{d}{dx} \sin(x) = \cos(x)

What is the derivative of cos⁡(x)\cos(x)?

ddxcos⁡(x)=−sin⁡(x)\frac{d}{dx} \cos(x) = -\sin(x)

How to differentiate tan⁡(x)\tan(x)?

ddxtan⁡(x)=sec⁡2(x)\frac{d}{dx} \tan(x) = \sec^2(x)

What is the derivative of ln⁡(x)\ln(x)?

ddxln⁡(x)=1x\frac{d}{dx} \ln(x) = \frac{1}{x}

How to differentiate exe^x?

ddxex=ex\frac{d}{dx} e^x = e^x

What is the chain rule formula?

dydx=f′(g(x))⋅g′(x)\frac{dy}{dx} = f'(g(x)) \cdot g'(x)

Differentiate ln⁡(2x+1)\ln(2x + 1)?

ddx=22x+1\frac{d}{dx} = \frac{2}{2x + 1}

Differentiate e4x2e^{4x^2}?

ddx=e4x2⋅8x\frac{d}{dx} = e^{4x^2} \cdot 8x

What is ddx\frac{d}{dx} of sec⁡(x)\sec(x)?

ddxsec⁡(x)=sec⁡(x)tan⁡(x)\frac{d}{dx} \sec(x) = \sec(x)\tan(x)

Differentiate y=tan⁡(ln⁡(x))y = \tan(\ln(x))?

ddx=sec⁡2(ln⁡(x))⋅1x\frac{d}{dx} = \sec^2(\ln(x)) \cdot \frac{1}{x}

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