Topic Review — Differentiation of Exponential and Logarithmic Functions

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This review covers all lessons in this topic: differentiating e^x, composite exponential functions, ln(x), and composite log functions with applications. Questions are mixed in difficulty.

Review Questions

1. Find d/dx[e^5x].
2. Find d/dx[ln(4x)].
3. Differentiate y = e^x².
4. Differentiate y = ln(2x + 5).
5. Find d/dx[3e^−2x].
6. Find the gradient of y = ln(x² + 3) at x = 1.
7. Use log laws to differentiate y = ln(x³(x+2)²).
8. Find the equation of the tangent to y = e^2x at x = 0.
9. Find the stationary point of y = e^−x + x and determine its nature.
10. State the domain of y = ln(3 − x) and find dy/dx.
11. Differentiate y = ln√(x+1) and simplify.
12. A quantity grows as Q = Q₀e^0.05t. Find dQ/dt and interpret it.
13. Find the stationary points of f(x) = x² − 2 ln x and classify each.
14. Find d/dx[e^x − e^−x].
15. A particle’s position is given by x(t) = ln(t² + 1). Find the velocity at t = 2 and determine when the particle is stationary.