3.9: Derivatives of Exponential and Logarithmic Functions
- Page ID
- 144213
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- Write \(\dfrac{b^{x}b^{x + 1}}{b^{2x}}\) as a single exponential expression.
- Write \(\dfrac{1}{2}\log_2(5x) + 15\log_2(x - 2) - 2\log_2(1 - x^2)\) as a single logarithmic expression.
- Expand \(\log_{10} \left(\dfrac{(2x - 3)^2(x + 1)}{\sqrt{x - 2}}\right)\).
- Calculate \(e^0\).
- Calculate \(\ln 1\).
- Calculate \(\ln e\).
- Simplify \(\ln(e^x)\).
- Simplify \(e^{\ln x}\).
- Find \(\displaystyle \lim_{x \to 0^+} \ln x\).
- Let \(f(x) = e^x\). What is the domain of \(f(x)\)? What is the range of \(f(x)\)?
- Let \(g(x) = \ln x\). What is the domain of \(g(x)\)? What is the range of \(g(x)\)?
- Rewrite the exponential expression \(3^{x^2 + 1}\) as an exponential expression with base \(e\).
- Rewrite the logarithmic expression \(\log_2(3x - 4)\) using the natural logarithm.
- Given \(f(x) = e^{x+1}\), find \(f'(x)\).
- Given \(f(x) = e^{2x^3 - 4x}\), find \(f'(x)\).
- Given \(f(x) = x^2 e^x\), find \(f'(x)\).
- Given \(f(x) = \dfrac{e^{-x}}{x}\), find \(f'(x)\).
- Given \(f(x) = 5^x\), find \(f'(x)\).
- Given \(f(x) = \dfrac{10^x}{\ln 10}\), find \(f'(x)\).
- Given \(f(x) = 3^{\sin 3x}\), find \(f'(x)\).
- Given \(f(x) = x^\pi \pi^x\), find \(f'(x)\).
- Given \(f(x) = \ln(x + 1)\), find \(f'(x)\).
- Given \(f(x) = \ln(4x^3 + x)\), find \(f'(x)\).
- Given \(f(x) = \ln \sqrt{5x - 7}\), find \(f'(x)\).
- Given \(f(x) = \ln(e^x)\), find \(f'(x)\).
- Given \(f(x) = \ln(\ln x)\), find \(f'(x)\).
- Given \(f(x) = x^2 \ln(x^2)\), find \(f'(x)\).
- Given \(f(x) = \dfrac{e^x}{\ln x}\), find \(f'(x)\).
- Given \(f(x) = \log_3\Bigl((5x^3 + 2x)^5\Bigr)\), find \(f'(x)\).
- Given \(y = x^x\), find \(\dfrac{dy}{dx}\).
- Given \(y = x^{\sin x}\), find \(\dfrac{dy}{dx}\).
- Given \(y = (\ln x)^{\ln x}\), find \(\dfrac{dy}{dx}\).
- Given \(y = (x^2 - 1)^{\cot x}\), find \(\dfrac{dy}{dx}\).
- Given \(y = x^{x^x}\), find \(\dfrac{dy}{dx}\).