f(x) = 4/5x

i need to find the derivitave but i don't know how to start this one. I know the derivitave of 4 is just zero, and i know the derivative of 5x is 5. But the answer isn't 0/5. Help please.

Hmmmm. do this..

f(x)=(4/5)*x-1

remember
g(t)=k t^n
g'=nk t^(n-1)

To find the derivative of the function f(x) = 4/5x, you can use the power rule. The power rule states that if you have a function of the form f(x) = ax^n, then the derivative is given by f'(x) = nax^(n-1).

In this case, we have f(x) = (4/5)x, which can be written as f(x) = (4/5)x^1. Applying the power rule, we can find the derivative as follows:

1. Multiply the coefficient (4/5) by the exponent (1) to get 4/5 * 1 = 4/5.

2. Subtract 1 from the exponent (1 - 1 = 0).

Therefore, the derivative of f(x) = 4/5x is f'(x) = 4/5x^0.

However, x^0 is equal to 1 for any value of x (except when x = 0, where it is undefined). Therefore, we can rewrite the derivative as:

f'(x) = 4/5 * 1 = 4/5.

So, the derivative of f(x) = 4/5x is f'(x) = 4/5.

To find the derivative of f(x) = 4/5x, you need to apply the power rule. The power rule states that the derivative of x^n is equal to n*x^(n-1).

In this case, we have f(x) = 4/5x, which can also be written as 4/5 * x^1.

To apply the power rule, you multiply the coefficient (4/5) by the exponent (1), and then decrease the exponent by 1.

Therefore, the derivative of f(x) = 4/5x is equal to (4/5) * 1 * x^(1-1) = 4/5 * x^0.

Now, anything raised to the power of 0 is equal to 1. So, x^0 = 1.

Hence, the derivative of f(x) = 4/5x is 4/5 * 1 = 4/5.

Thus, the answer is not 0/5, it is indeed 4/5.