Differentiation and its Applications
CBSE · Class 12 · Applied Mathematics
Quick revision notes for Differentiation and its Applications — CBSE Class 12 Applied Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Differentiation of Implicit Functions
- Implicit functions are equations where y cannot be expressed explicitly as y = f(x)
- We differentiate both sides of the equation with respect to x, treating y as a function of x
- Use chain rule: d/dx(y²) = 2y·dy/dx
Differentiation of Parametric Functions
- Parametric equations express both x and y in terms of a parameter t: x = f(t), y = g(t)
- dy/dx = (dy/dt)/(dx/dt), provided dx/dt ≠ 0
- Common parametric forms include circles, parabolas, and cycloids
Logarithmic Differentiation
- Used for functions of the form [f(x)]^g(x) where both base and exponent contain x
- Take natural logarithm of both sides before differentiating
- Apply product rule to log y = g(x)·log f(x)
Second and Higher Order Derivatives
- Second derivative: d²y/dx² = d/dx(dy/dx)
- Third derivative: d³y/dx³ = d/dx(d²y/dx²)
- Higher order derivatives: d^n y/dx^n = f^(n)(x)
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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