what is the derivative of f(x)= x ... is it 1??
yes
thank you ...
Yes, you are correct! The derivative of the function f(x) = x is equal to 1.
To explain how we can arrive at this answer, let's use the definition of the derivative. The derivative of a function measures how the function changes with respect to its variable. In this case, we want to find how the function f(x) = x changes as x changes.
The derivative of a function f(x) at a point x is represented as f'(x) or dy/dx. It measures the slope of the tangent line to the function at that point.
To find the derivative of f(x) = x, we can use a basic rule of differentiation. The power rule states that the derivative of x raised to any power n is equal to n times x raised to the power n-1.
In this case, the power of x is 1, so using the power rule, we have:
f'(x) = 1 * x^(1-1) = 1 * x^0 = 1 * 1 = 1.
Therefore, the derivative of f(x) = x is 1 at any point x.