Determine \frac{dy}{dx}.
y = \log_5x
Determine \frac{dy}{dx}.
y = \log_3x
Determine \frac{dy}{dx}.
y = 2\log_4x
Determine \frac{dy}{dx}.
y = -3\log_7x
Determine \frac{dy}{dx}.
y = -(\log x)
Determine \frac{dy}{dx}.
y = 3\log_6x
Determine the derivative.
y = \log_3(x + 2)
Determine the derivative.
y = \log_8(2x)
Determine the derivative.
\displaystyle
y = - 3\log_3(2x + 3)
Determine the derivative.
y = \log_{10}(5-2x)
Determine the derivative.
y = \log_8(2x+ 6)
Determine the derivative.
y = \log_{7}(x^2 + x + 1)
If f(t) = \log_2(\frac{t + 1}{2t + 7}), evaluate f'(3).
If h(t) = \log_3(\log_2(t)), determine h'(8).
Differentiate.
\displaystyle
f(x) = \log_{10}(\frac{1 + x }{1- x})
Differentiate.
\displaystyle
y = \log_2\sqrt{x^2 + 3x}
Differentiate.
\displaystyle
y = 2\log_3(5^x) -\log_3(4^x)
Differentiate.
\displaystyle
g(x) = 3^x\log_3x
Differentiate.
\displaystyle
y = 2x \log_4x
Differentiate.
\displaystyle
y = \frac{\log_5(3x^2)}{\sqrt{x + 1}}
Determine the equation of the tangent to the curve y = x\log x at x = 10. Graph the function and the tangent.
Explain why the derivative of y = \log_akx, k > 0, is \frac{dy}{dx} = \frac{1}{x\ln a} for any constant k.
Determine the domain, critical numbers, and intervals of increase and decrease of f(x) = \ln(x^2 -4).
Do the graphs of either of these functions have points of inflection? Justify your answers with supporting calculations.
a) y = x\ln x
b) y = 3-2\log x
Determine whether the slope of the graph of
y = 3^x at the point (0, 1) is greater than the
slope of the graph of y = \log_3x at the point (1, 0).
Include graphs with your solution.