What is the first (5/(x^5))^' ?

The first (5/(x^5))^' is -(25)/(x^6)

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(5/(x^5))^'

(\frac{5}{x ^{5}})^{^{'}}

- \frac{25}{x ^{6}}

Solution steps

(\frac{5}{x ^{5}})^{'}

Take the constant out:

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

= 5 (\frac{1}{x ^{5}})^{^{'}}

Apply exponent rule:

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

= 5 (x^{- 5})^{^{'}}

Apply the Power Rule:

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

= 5 (- 5 x^{- 5 - 1})

Simplify

5 (- 5 x^{- 5 - 1}) : - \frac{25}{x ^{6}}

= - \frac{25}{x ^{6}}

2 y = 3 x, y = 3, 2 y + 4 x = 7

\int_{0}^{\frac{π}{4}} 1 + tan (x) d x

\frac{d}{d x} (\frac{6 x}{x ^{2} - 9})

y^{^{'}} = (3 x - 2) (30 x + 29)

\frac{d y}{d x}, 9 x^{2} + y^{2} = 1