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I can't figure out
Derivative of (sq. rt of x)^x
Can anyone help me?
Derivative of (sq. rt of x)^x
Can anyone help me?
djeitnstine said:Welcome to PF =]
Use the chain rule, this is simply a function within another function. the outer function just happens to be an exponential. [tex]\frac{d}{dx}f^x=f^x ln(f)[/tex] (if I remember correctly)
The derivative of the square root of x is equal to 1 over 2 times the square root of x. This can be written as 1/(2√x) or (x^1/2)/2.
To find the derivative of a function involving a square root, you can use the power rule and the chain rule. First, rewrite the function as (x^1/2) and then apply the power rule to get (1/2)x^(-1/2). Next, use the chain rule by multiplying the derivative by the derivative of what's inside the square root (1/2x). This results in a final derivative of 1/(2√x).
Yes, the derivative of the square root of x can be negative. This means that the function is decreasing at that point. However, the value of x must be positive in order for the square root to be defined.
The derivative of the square root of a constant is equal to 0. This is because a constant value does not change with respect to x, so its derivative is always 0.
Yes, the derivative of the square root of x is the same as the derivative of x^(1/2). This is because they are two different ways of representing the same function, with the exponent of 1/2 indicating the square root. Therefore, the derivative will be the same for both representations.