What is the derivative of 5/((6x+5^2)) ?

The derivative of 5/((6x+5^2)) is -(60)/((6x+5)^3)

What is the first derivative of 5/((6x+5^2)) ?

The first derivative of 5/((6x+5^2)) is -(60)/((6x+5)^3)

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\frac{d}{d x} (\frac{5}{( 6 x + 5 ) ^{2}})

- \frac{60}{( 6 x + 5 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{5}{( 6 x + 5 ) ^{2}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{( 6 x + 5 ) ^{2}})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((6 x + 5)^{- 2})

Apply the chain rule:

- \frac{2}{( 6 x + 5 ) ^{3}} \frac{d}{d x} (6 x + 5)

= - \frac{2}{( 6 x + 5 ) ^{3}} \frac{d}{d x} (6 x + 5)

\frac{d}{d x} (6 x + 5) = 6

= 5 (- \frac{2}{( 6 x + 5 ) ^{3}} \cdot 6)

Simplify

5 (- \frac{2}{( 6 x + 5 ) ^{3}} \cdot 6) : - \frac{60}{( 6 x + 5 ) ^{3}}

= - \frac{60}{( 6 x + 5 ) ^{3}}

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

y = - x^{2} + 1, (0, 1)

\frac{7 x + 1}{2 x - 3}

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What is the derivative of 5/((6x+5^2)) ?
The derivative of 5/((6x+5^2)) is -(60)/((6x+5)^3)
What is the first derivative of 5/((6x+5^2)) ?
The first derivative of 5/((6x+5^2)) is -(60)/((6x+5)^3)