All the worked exercises of the chapter, in order of appearance in the book: derivatives with the rules and the circle diagram, points of non-differentiability, Taylor expansions, the theorems of calculus, function studies and optimisation problems.
- Derivative of x³ ln x
- Derivative of the quotient eˣ over (x²+1)
- Derivative of ln(sin(x³))
- Derivative of e to the cos(2x)
- Tangent and normal to eˣ
- Derivative of arctan(√x)
- Derivative of (1+x²) to the tenth
- Derivative of ln of the absolute value of x
- Classifying points of non-differentiability
- Corner point of ln x in modulus
- Parameter for differentiability
- Differentiability of x·∛x
- Graph with corner, cusp and vertical tangent
- Maclaurin polynomial of e to the 2x
- Limit (eˣ−1−x) over x²
- Estimate of √1,1 with Taylor
- Maclaurin of tan x
- Limit (sin x − x cos x) over x³
- Taylor polynomial of ln x at x₀=1
- Study of (x²−1) over (x²+1)
- Study of x·e to the −x
- Study of ln(x²−4)
- Rolle’s theorem
- Lagrange’s theorem
- Rectangle inscribed in a semicircle
- Limit with De L’Hôpital
- Parametric study of x over (x²+k)