MSBTE Diploma Math: Score Max Marks in Derivatives (Step-by-Step)

Problems Covered:
1. Parametric Differentiation:
Find dy/dx if x = a cos³θ, y = b sin³θ.
We'll show you how to find the derivative of functions defined parametrically.
2. Chain Rule:
Differentiate with respect to x: y = 7^√(x²+1).
A classic example demonstrating the power of the chain rule.
3. Inverse Trigonometric Functions:
If y = tan⁻¹((1-4x²)/(1+4x²)), find dy/dx.
Learn how to differentiate complex inverse trigonometric functions.
4. Substitution Method (Inverse Trig):
If y = sin⁻¹(2x/(1+x²)), find dy/dx.
We use a clever trigonometric substitution to simplify the problem and find the derivative.
5. Implicit Differentiation:
Find dy/dx if sin y = log(x + y).
This problem requires implicit differentiation to find the derivative when y is not explicitly defined in terms of x.
6. Proof Problem:
If e^y = y^x, prove that dy/dx = (log y)² / (log y - 1).
A logarithmic differentiation problem that involves a proof.
7. Logarithmic Differentiation:
Differentiate (sin x)^tan x with respect to x.
This is a perfect example for using logarithmic differentiation to handle functions with both a variable base and a variable exponent.
8. Differentiating w.r.t. another function:
Differentiate tan⁻¹(2x/(1-x²)) with respect to sin⁻¹(2x/(1+x²)).
Learn how to find the derivative of one function relative to another function.

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Please watch: "Adjacency Matrix and Incidence Matrix in Graph Theory (Discrete Mathematics) Solved ‪@lakichand99‬ "
https://www.youtube.com/watch?v=A9VejK6v5AY
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Видео MSBTE Diploma Math: Score Max Marks in Derivatives (Step-by-Step) канала Laki Academy 🌐