Calculus & Analysis formula — definition, units and applicable conditions

found 4formulas · currently displayed 4Articles Explanation · Unit · Applicable conditions

Calculus & Analysis

derivative definition

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}

describes the instantaneous rate of change with the limit of the local difference quotient.

Calculus & Analysis

\int_a^b f(x)\,dx=F(b)-F(a),\quad F'=f

Calculates the definite integral using the boundary difference of the original function.

Calculus & Analysis

\frac{d}{dx}f(g(x))=f'(g(x))g'(x)

composite function is equal to the product of the local change rates of each layer.

Calculus & Analysis

\int_a^b u v'\,dx=[uv]_a^b-\int_a^b u'v\,dx

rewrites the product differential rule into an integral calculation method.