Answer:
To find the derivative of the function y = √(5x^4), we can use the power rule and chain rule of differentiation. The power rule states that if we have a function of the form f(x) = x^n, then its derivative is given by f'(x) = nx^(n-1). The chain rule allows us to differentiate composite functions.
Let's begin by rewriting the function as y = 5^(1/2) * x^(4/2). Now, applying the power rule, we can differentiate each term separately. The derivative of 5^(1/2) is 0 since it is a constant. For the second term, x^(4/2) can be simplified to x^2. Applying the power rule, we find that the derivative of x^2 is 2x.
Therefore, the derivative of y = √(5x^4) is dy/dx = 0 + 2x = 2x.
In summary, the derivative of y = √(5x^4) with respect to x is 2x.
Explanation: