Derivatives of Logarithmic Functions
Explore and practice finding derivatives of various logarithmic functions, including natural logarithms and those with different bases, at a Grade 12 Calculus level.
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Derivatives of Logarithmic Functions
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Read each question carefully and show all your work. Simplify your answers where possible.
Find the derivative of each function with respect to x.
1. f(x) = ln(x^3 + 2x)
2. g(x) = log_5(x^2 - 4)
3. h(x) = x ln(x)
Apply the chain rule to find the derivative of the following functions.
1. y = ln(cos(x))
2. y = log_2(sin(x^2))
Complete the steps to find the derivative of y = x^sin(x) using logarithmic differentiation.
Take the natural logarithm of both sides: ln(y) =
Differentiate implicitly with respect to x: (1/y) * (dy/dx) =
Solve for dy/dx: dy/dx =
1. If f(x) = ln(e^(2x)), then f'(x) is:
1/e^(2x)
2
2e^(2x)
e^(2x)
The population P of a certain bacterial colony at time t (in hours) is given by P(t) = 1000 ln(t^2 + 1). Find the rate of change of the population at t = 3 hours.