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

The derivative of 5/((3x^2-x)^4) is -(20(6x-1))/((3x^2-x)^5)

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

The first derivative of 5/((3x^2-x)^4) is -(20(6x-1))/((3x^2-x)^5)

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derivative of

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

- \frac{20 ( 6 x - 1 )}{( 3 x ^{2} - x ) ^{5}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 (- \frac{4}{( 3 x ^{2} - x ) ^{5}} (6 x - 1)) : - \frac{20 ( 6 x - 1 )}{( 3 x ^{2} - x ) ^{5}}

= - \frac{20 ( 6 x - 1 )}{( 3 x ^{2} - x ) ^{5}}

\frac{d}{d x} (\frac{1}{x - a})

(1 - e^{- a x})^{2}

\frac{3 e ^{(- 2 s)}}{( s ^{2} - 4 s + 3 )}

ln (100 sin^{2} (x))

f (x) = \frac{4 x ^{2} tan ( x )}{sec ( x )}

What is the derivative of 5/((3x^2-x)^4) ?
The derivative of 5/((3x^2-x)^4) is -(20(6x-1))/((3x^2-x)^5)
What is the first derivative of 5/((3x^2-x)^4) ?
The first derivative of 5/((3x^2-x)^4) is -(20(6x-1))/((3x^2-x)^5)