7/5√x^2 find derivative

Answer 1

To find the derivative of the function, we can use the power rule and the chain rule.

Let's denote the given function as f(x) = 7/5√x^2.

Using the power rule, we can write f(x) as f(x) = 7/5 * (x^2)^(1/2).

Now, let's take the derivative with respect to x:

f'(x) = (7/5) * (1/2) * (x^2)^(1/2 - 1) * 2x
= (7/5) * (1/2) * x (x^2)^(-1/2) * 2x
= (7/5) * (1/2) * 2x * x^(-1/2)
= 7/5 * x * x^(-1/2)
= 7/5 * x^(1/2)

Therefore, the derivative of f(x) = 7/5√x^2 is f'(x) = 7/5 * x^(1/2).