What is the derivative of f(x)= 6/(sqrt(x)) ?

The derivative of f(x)= 6/(sqrt(x)) is -3/(x^{3/2)}

What is the first derivative of f(x)= 6/(sqrt(x)) ?

The first derivative of f(x)= 6/(sqrt(x)) is -3/(x^{3/2)}

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derivative of

f (x) = \frac{6}{x}

- \frac{3}{x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{6}{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 6 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 6 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

6 (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{3}{x ^{\frac{3}{2}}}

= - \frac{3}{x ^{\frac{3}{2}}}

\frac{\partial}{\partial x} ((x - y)^{5})

y = \frac{8}{x ^{2} + 4}, (2, 1)

\int_{1}^{2} \frac{1}{8} + \frac{3}{8} x d x

\frac{d}{d x} ((3 x^{4} - x + 1) (- x^{5} + 4))

y^{^{'}} + 2 y = 1, y (0) = \frac{5}{2}

What is the derivative of f(x)= 6/(sqrt(x)) ?
The derivative of f(x)= 6/(sqrt(x)) is -3/(x^{3/2)}
What is the first derivative of f(x)= 6/(sqrt(x)) ?
The first derivative of f(x)= 6/(sqrt(x)) is -3/(x^{3/2)}