What is the derivative of (-9/(2x^5)) ?

The derivative of (-9/(2x^5)) is (45)/(2x^6)

What is the first derivative of (-9/(2x^5)) ?

The first derivative of (-9/(2x^5)) is (45)/(2x^6)

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\frac{d}{d x} (\frac{- 9}{2 x ^{5}})

\frac{45}{2 x ^{6}}

Solution steps

\frac{d}{d x} (\frac{- 9}{2 x ^{5}})

Simplify

\frac{- 9}{2 x ^{5}} : - \frac{9}{2 x ^{5}}

= \frac{d}{d x} (- \frac{9}{2 x ^{5}})

Take the constant out:

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

= - \frac{9}{2} \frac{d}{d x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= - \frac{9}{2} \frac{d}{d x} (x^{- 5})

Apply the Power Rule:

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

= - \frac{9}{2} (- 5 x^{- 5 - 1})

Simplify

- \frac{9}{2} (- 5 x^{- 5 - 1}) : \frac{45}{2 x ^{6}}

= \frac{45}{2 x ^{6}}

\frac{d y}{d x} = 1 - y^{2}

f (x) = 12 x, at x = 1

\frac{\partial}{\partial y} (\frac{x y z ^{2}}{x y + 1})

f (x) = 6 x, (6, 6)

\frac{30 s + 102}{s ^{2} + 4 s + 40}

What is the derivative of (-9/(2x^5)) ?
The derivative of (-9/(2x^5)) is (45)/(2x^6)
What is the first derivative of (-9/(2x^5)) ?
The first derivative of (-9/(2x^5)) is (45)/(2x^6)