Commission Brokerage and Discount
Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce
Quick revision notes for Commission Brokerage and Discount — Maharashtra Board Class 12 Mathematics & Statistics -Commerce. Key concepts, formulas, and definitions for last-minute revision.
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Key Topics to Revise
Derivatives of Composite Functions (Chain Rule)
- If y = f(u) and u = g(x), then dy/dx = (dy/du) × (du/dx)
- Chain rule is essential for differentiating nested functions
- Always identify the outer and inner functions clearly
Derivatives of Inverse Functions
- If y = f(x) and x = f⁻¹(y), then dx/dy = 1/(dy/dx)
- Derivative of inverse function is reciprocal of derivative of original function
- Domain and range considerations are crucial
Logarithmic Differentiation
- Take natural log of both sides, then differentiate
- Useful for functions with products, quotients, and powers
- Essential for functions of the form y = [f(x)]^g(x)
Derivatives of Implicit Functions
- Differentiate both sides with respect to x, treating y as function of x
- Use dy/dx notation consistently throughout
- Collect all terms containing dy/dx on one side
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