Fundamental Rules for Differentiation
( v) if d / d( x) f( x) = φ( x), then d / d( x) f( ax + b) = a φ( ax + b)( vi) Differentiation of a constant function is zero i. e., d / d( x)( c) = 0. Geometrically Meaning of Derivative at a Point
Geometrically derivative of a function at a point x = c is the slope of the tangent to the curve y = f( x) at the point { c, f( c)}.
Slope of tangent at P = lim x → c f( x) – f( c) / x – c = { df( x) / d( x)} x = c or f’( c). Different Types of Differentiable Function 1. Differentiation of Composite Function( Chain Rule)
If f and g are differentiable functions in their domain, then fog is also differentiable and
( fog)’( x) = f’ { g( x)} g’( x) More easily, if y = f( u) and u = g( x), then dy / dx = dy / du * du / dx.