f ( x ) = x 3 − 4 x d d x [ x 3 − 4 x ] = d d x [ x 3 ] − 4 ⋅ d d x [ x ] = 3 x 2 − 4 ⋅ 1 = 3 x 2 − 4 f ( x ) = x 3 5 d d x [ x 3 5 ] = 3 5 ⋅ x 3 5 − 1 = 3 5 x 2 5
A function which gives the slope of a curve; that is, the slope of the line tangent to a function. The derivative of a function f at a point x is commonly written f'(x). For example, if f(x) = x3 then f '(x) = 3x2. The slope of the tangent line when x = 5 is f '(x) = 3·52 = 75. Formula: