Further Differentiation (AQA A-Level Mathematics): Flashcards

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Differentiating Other Functions (Trig, ln & e etc)
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ddx[sin⁡(x)]\frac{d}{dx}[\sin(x)]

cos⁡(x)\cos(x)

ddx[cos⁡(x)]\frac{d}{dx}[\cos(x)]

−sin⁡(x)-\sin(x)

ddx[tan⁡(x)]\frac{d}{dx}[\tan(x)]

sec⁡2(x)\sec^2(x)

ddx[ln⁡(x)]\frac{d}{dx}[\ln(x)]

1x\frac{1}{x}

ddx[ex]\frac{d}{dx}[e^x]

exe^x

ddx[ax]\frac{d}{dx}[a^x] where aa is constant

axln⁡(a)a^x \ln(a)

ddx[eu(x)]\frac{d}{dx}[e^{u(x)}]

eu(x)⋅u′(x)e^{u(x)} \cdot u'(x)

ddx[ln⁡(u(x))]\frac{d}{dx}[\ln(u(x))]

u′(x)u(x)\frac{u'(x)}{u(x)}

ddx[sin⁡(3x)]\frac{d}{dx}[\sin(3x)]

3cos⁡(3x)3\cos(3x)

ddx[ln⁡(2x+1)]\frac{d}{dx}[\ln(2x+1)]

22x+1\frac{2}{2x+1}

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