What is the derivative of (-5/(2x^6-4x^3-6x)) ?

The derivative of (-5/(2x^6-4x^3-6x)) is (15(2x^5-2x^2-1))/(2x^2(x^5-2x^2-3)^2)

What is the first derivative of (-5/(2x^6-4x^3-6x)) ?

The first derivative of (-5/(2x^6-4x^3-6x)) is (15(2x^5-2x^2-1))/(2x^2(x^5-2x^2-3)^2)

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\frac{d}{d x} (\frac{- 5}{2 x ^{6} - 4 x ^{3} - 6 x})

\frac{15 ( 2 x ^{5} - 2 x ^{2} - 1 )}{2 x ^{2} ( x ^{5} - 2 x ^{2} - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 5}{2 x ^{6} - 4 x ^{3} - 6 x})

Simplify

\frac{- 5}{2 x ^{6} - 4 x ^{3} - 6 x} : - \frac{5}{2 x ^{6} - 4 x ^{3} - 6 x}

= \frac{d}{d x} (- \frac{5}{2 x ^{6} - 4 x ^{3} - 6 x})

Take the constant out:

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

= - 5 \frac{d}{d x} (\frac{1}{2 x ^{6} - 4 x ^{3} - 6 x})

Apply exponent rule:

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

= - 5 \frac{d}{d x} ((2 x^{6} - 4 x^{3} - 6 x)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} \frac{d}{d x} (2 x^{6} - 4 x^{3} - 6 x)

= - \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} \frac{d}{d x} (2 x^{6} - 4 x^{3} - 6 x)

\frac{d}{d x} (2 x^{6} - 4 x^{3} - 6 x) = 12 x^{5} - 12 x^{2} - 6

= - 5 (- \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} (12 x^{5} - 12 x^{2} - 6))

Simplify

- 5 (- \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} (12 x^{5} - 12 x^{2} - 6)) : \frac{15 ( 2 x ^{5} - 2 x ^{2} - 1 )}{2 x ^{2} ( x ^{5} - 2 x ^{2} - 3 ) ^{2}}

= \frac{15 ( 2 x ^{5} - 2 x ^{2} - 1 )}{2 x ^{2} ( x ^{5} - 2 x ^{2} - 3 ) ^{2}}

What is the derivative of (-5/(2x^6-4x^3-6x)) ?
The derivative of (-5/(2x^6-4x^3-6x)) is (15(2x^5-2x^2-1))/(2x^2(x^5-2x^2-3)^2)
What is the first derivative of (-5/(2x^6-4x^3-6x)) ?
The first derivative of (-5/(2x^6-4x^3-6x)) is (15(2x^5-2x^2-1))/(2x^2(x^5-2x^2-3)^2)