Agniveer (All) Differentiation

If y = f(x), then dy/dx represents the derivative of y with respect to x. This derivative gives us the slope of the tangent line at any point on the curve

d/dx(x^n) = n × x^(n-1) 2

d/dx(c) = 0 (where c is constant) 3

d/dx(u + v) = du/dx + dv/dx 4

d/dx(uv) = u(dv/dx) + v(du/dx) 5

d/dx(u/v) = [v(du/dx) - u(dv/dx)]/v² 6

d/dx[f(g(x))] = f'(g(x)) × g'(x) Standard Derivatives (Must Memorize): - d/dx(sin x) = cos x - d/dx(cos x) = -sin x - d/dx(tan x) = sec²x - d/dx(e^x) = e^x - d/dx(ln x) = 1/x - d/dx(a^x) = a^x × ln a

Direct differentiation of polynomials, trigonometric, and exponential functions 2. Composite functions requiring chain rule 3. Word problems involving rates of change 4. Finding equation of tangent/normal at given points Shortcut for Chain Rule: Remember the 'outside-inside' method.

Differentiate the outer function first, keep the inner function unchanged, then multiply by the derivative of the inner function

For simple powers like (ax + b)^n, use the formula: derivative = n(ax + b)^(n-1) × a. This saves time compared to full chain rule expansion

Students forget to apply the chain rule when dealing with composite functions. For example, when differentiating sin(2x), many write cos(2x) instead of 2cos(2x). Always check if there's an 'inner function' and multiply by its derivative. Another frequent error is sign mistakes in trigonometric derivatives. Remember that d/dx(cos x) = -sin x (negative sign), not +sin x. For NDA success, practice mixed problems daily.

Focus on recognizing patterns quickly - whether to use power rule, product rule, or chain rule. Speed and accuracy in basic derivatives will save precious exam time for complex application problems.