What is the derivative of y= 3/(sqrt(x)) ?

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

What is the first derivative of y= 3/(sqrt(x)) ?

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

derivative of

y = \frac{3}{x}

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

Solution steps

\frac{d}{d x} (\frac{3}{x})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 3 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

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

Simplify

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

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

y^{^{'}} = 3 x^{2} e^{- y}

\int \frac{1}{x ln ( x ^{6} )} d x

\int \frac{x}{( x + 5 ) ^{2}} d x

\frac{d}{d x} ((12 x^{2} - 24 x + 24) e^{x})

\frac{d}{d x} ((\frac{2}{3})^{x})

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