f'(x)/f(x) (AQA A-Level Mathematics): Flashcards

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f'(x)/f(x)
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f′(x)f(x)\frac{f'(x)}{f(x)} is the derivative of?

ln⁡∣f(x)∣\ln|f(x)|

ddx[ln⁡∣f(x)∣]\frac{d}{dx}[\ln|f(x)|] equals?

f′(x)f(x)\frac{f'(x)}{f(x)}

Rule used to find ddx[ln⁡∣f(x)∣]\frac{d}{dx}[\ln|f(x)|]?

Chain rule

ddx[ln⁡∣f(x)∣]\frac{d}{dx}[\ln|f(x)|] before simplification?

1f(x)⋅f′(x)\frac{1}{f(x)} \cdot f'(x)

∫f′(x)f(x) dx\int \frac{f'(x)}{f(x)} \, dx equals?

ln⁡∣f(x)∣+C\ln|f(x)| + C

For f(x)=x2+1f(x) = x^2 + 1, what is f′(x)f'(x)?

2x2x

For f(x)=x2+1f(x) = x^2 + 1, what is f′(x)f(x)\frac{f'(x)}{f(x)}?

2xx2+1\frac{2x}{x^2 + 1}

∫2xx2+1 dx\int \frac{2x}{x^2 + 1} \, dx equals?

ln⁡∣x2+1∣+C\ln|x^2 + 1| + C

Application area of f′(x)f(x)\frac{f'(x)}{f(x)} result?

Logarithmic differentiation

Another application of f′(x)f(x)\frac{f'(x)}{f(x)} result?

Logarithmic integration

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