What is the derivative of the function f(x)= 4 over x square root of x

Question

asked Sep 20, 2024 116k views

1 Answer

You Kuper · Answer 1 · 2024-09-27T04:38:26+0000

Answer:

f'(x) = -2/√(x³)

Explanation:

You want the derivative of f(x) = 4/√x.

The power rule for derivatives is ...

(d)/(dx)(x^n)=nx^((n-1))

Applied to the given function, we have ...

$f(x)=(4)/(√(x))=4x^{-(1)/(2)}\\\\f'(x)=4(-(1)/(2)x^{-(3)/(2)})\\\\\boxed{f'(x)=-(2)/(√(x^3))}$

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Additional comment

The first attachment shows a calculator gives the same result.

The second attachment shows the derivative curve matches the one described by the function we found.