chief12 said:Homework Statement
function f is differential when x=0,
f'(0) is not equal to zero for all a,b(real Numbers)
f(a+b) = f(a)f(b)
show f'(x) = f'(x)f(x)
A derivative is a mathematical concept that represents the rate of change of one quantity with respect to another. It is defined as the slope of a tangent line to a curve at a specific point.
To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. Alternatively, you can also use the definition of a derivative to calculate it.
Finding derivatives is important in mathematics because it allows us to understand the behavior of a function, such as its rate of change, concavity, and critical points. It also has many applications in fields such as physics, engineering, and economics.
A derivative is a function that represents the rate of change of another function, while a differential is an infinitesimal change in a variable. In other words, a derivative is a concept, while a differential is a quantity.
Yes, derivatives can be extended to multivariable functions, resulting in partial derivatives. These represent the rate of change of one variable with respect to another, while holding all other variables constant. Higher order derivatives, such as second or third derivatives, can also be calculated for multivariable functions.