Differentiation of Logarithmic Functions (HSC SSCE Mathematics Advanced): Quizzes

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Differentiation of Logarithmic Functions
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What is ddxlog⁡ex\frac{d}{dx} \log_e x?

1x\frac{1}{x}

What is the domain of y=log⁡exy = \log_e x?

x>0x > 0

Where does y=log⁡exy = \log_e x cross the xx-axis?

At x=1x = 1

What is the second derivative of y=log⁡exy = \log_e x?

−1x2-\frac{1}{x^2}

What is the gradient of y=log⁡exy = \log_e x at its xx-intercept?

11

What is ddxlog⁡e(5x+2)\frac{d}{dx} \log_e(5x + 2)?

55x+2\frac{5}{5x + 2}

What is ddxlog⁡e(x2+1)\frac{d}{dx} \log_e(x^2 + 1)?

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

Simplify log⁡e(3x−7)5\log_e(3x - 7)^5 before differentiating. What is the simplified form?

5log⁡e(3x−7)5\log_e(3x - 7)

After simplifying log⁡e(1+x1−x)\log_e\left(\frac{1 + x}{1 - x}\right) using log laws, what do you get?

log⁡e(1+x)−log⁡e(1−x)\log_e(1 + x) - \log_e(1 - x)

What is the range of y=log⁡exy = \log_e x?

All real numbers

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