Differentiation Solve Problems

Introduction

Calculus is a branch of mathematics developed from algebra and geometry built on two major complimentary ideas. The first idea is called differentiation and the second one integration.

Here we deals with the first major concept called differentiation which is about a vast generalisation of the slope of a line. It is the rate of change of a quantity. It permits velocity, acceleration and slope of a curve at a given point.

Differentiation is a main technique in calculus to find the derivative. Derivative is a measure of how a function changes as its input changes. A derivative can be thought of as how much one quantity is changing in response to changes in some other quantity. For a real valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. The process of finding the derivative is called differentiation.

Rules for differentiation

There are mainly 5 rules used for solving problems.

• Constant rule : If f(x) is a constant, then f' = 0.
• Sum rule : If f and g are two functions and a and b are two real numbers, then (af + bg)' = af' + bg'.
• Product rule : (fg)' = f'g + fg' For all f and g.
• Quotient rule : (f/g)' = (f'g -fg')/g²for all functions f and g where g#0
• Chain rule : If f(x) = h g(x), then f'(x) = h'(g(x)). g'(x)