What is the derivative of (-2(x-9))/(x^4) ?

The derivative of (-2(x-9))/(x^4) is -(6(-x+12))/(x^5)

What is the first derivative of (-2(x-9))/(x^4) ?

The first derivative of (-2(x-9))/(x^4) is -(6(-x+12))/(x^5)

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derivative of

\frac{- 2 ( x - 9 )}{x ^{4}}

- \frac{6 ( - x + 12 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{- 2 ( x - 9 )}{x ^{4}})

Simplify

\frac{- 2 ( x - 9 )}{x ^{4}} : - \frac{2 ( x - 9 )}{x ^{4}}

= \frac{d}{d x} (- \frac{2 ( x - 9 )}{x ^{4}})

Take the constant out:

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

= - 2 \frac{d}{d x} (\frac{x - 9}{x ^{4}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 2 \cdot \frac{\frac{d}{d x} ( x - 9 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( x - 9 )}{( x ^{4} ) ^{2}}

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

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

= - 2 \cdot \frac{1 \cdot x ^{4} - 4 x ^{3} ( x - 9 )}{( x ^{4} ) ^{2}}

Simplify

- 2 \cdot \frac{1 \cdot x ^{4} - 4 x ^{3} ( x - 9 )}{( x ^{4} ) ^{2}} : - \frac{6 ( - x + 12 )}{x ^{5}}

= - \frac{6 ( - x + 12 )}{x ^{5}}

\int \frac{3 x + 12}{x ^{3} + 4 x ^{2} + 4 x} d x

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

\int_{- 1}^{2} 3 x^{2} + 6 x d x

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

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

What is the derivative of (-2(x-9))/(x^4) ?
The derivative of (-2(x-9))/(x^4) is -(6(-x+12))/(x^5)
What is the first derivative of (-2(x-9))/(x^4) ?
The first derivative of (-2(x-9))/(x^4) is -(6(-x+12))/(x^5)