7/5√x^2 find derivative
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).
To find the derivative of the function 7/(5√x^2), we can use the quotient rule.
The quotient rule states that if we have a function in the form f(x)/g(x), where f(x) and g(x) are both differentiable functions, then the derivative of the function is given by:
(f'(x)g(x) - g'(x)f(x)) / (g(x))^2
In this case, f(x) = 7 and g(x) = 5√x^2. Let's find the derivatives:
f'(x) = 0, since the derivative of a constant is zero.
g'(x) = (5/2) * (2x^1/2), using the power rule for differentiation.
Now, we can substitute these values into the quotient rule:
(0 * 5√x^2 - (5/2) * (2x^1/2) * 7) / (5√x^2)^2
Simplifying this expression, we get:
-(35x^1/2) / (25x)
Therefore, the derivative of 7/(5√x^2) is -(35x^1/2) / (25x).