What is the derivative of (12/(sqrt(x))) ?

The derivative of (12/(sqrt(x))) is -6/(x^{3/2)}

What is the first derivative of (12/(sqrt(x))) ?

The first derivative of (12/(sqrt(x))) is -6/(x^{3/2)}

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\frac{d}{d x} (\frac{12}{x})

- \frac{6}{x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{12}{x})

Take the constant out:

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

= 12 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 12 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

= 12 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

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

= - \frac{6}{x ^{\frac{3}{2}}}

ln (3) - ln (x^{3} - 4 x + 2)

\int_{0}^{4} \frac{1}{x ^{2} - 16} d x

x \to 4 lim (\frac{5 - x}{x - 4})

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\frac{d}{d x} (c e^{5 t} + c e^{5 y (t, x)})

What is the derivative of (12/(sqrt(x))) ?
The derivative of (12/(sqrt(x))) is -6/(x^{3/2)}
What is the first derivative of (12/(sqrt(x))) ?
The first derivative of (12/(sqrt(x))) is -6/(x^{3/2)}