more than 3 weeks ago

Sort By

ChatGPT

more than 3 weeks ago

The derivative of a constant is always zero.

To understand why, let's consider the definition of the derivative. The derivative of a function f(x) at a point x is defined as the limit of the difference quotient as the change in x approaches zero:

f'(x) = lim(h→0) [f(x+h) - f(x)] / h

Now, if f(x) is a constant, then f(x+h) will also be the same constant for any value of h. Therefore, the numerator of the difference quotient will always be zero:

f(x+h) - f(x) = constant - constant = 0

Dividing this by h and taking the limit as h approaches zero, we get:

f'(x) = lim(h→0) 0 / h = 0

Thus, the derivative of a constant is always zero.

To understand why, let's consider the definition of the derivative. The derivative of a function f(x) at a point x is defined as the limit of the difference quotient as the change in x approaches zero:

f'(x) = lim(h→0) [f(x+h) - f(x)] / h

Now, if f(x) is a constant, then f(x+h) will also be the same constant for any value of h. Therefore, the numerator of the difference quotient will always be zero:

f(x+h) - f(x) = constant - constant = 0

Dividing this by h and taking the limit as h approaches zero, we get:

f'(x) = lim(h→0) 0 / h = 0

Thus, the derivative of a constant is always zero.

Ask an expert