What is the derivative of 5/(x^3-2/(x^2)-1/x+200) ?

The derivative of 5/(x^3-2/(x^2)-1/x+200) is 4/(x^3)+1/(x^2)-(15)/(x^4)

What is the first derivative of 5/(x^3-2/(x^2)-1/x+200) ?

The first derivative of 5/(x^3-2/(x^2)-1/x+200) is 4/(x^3)+1/(x^2)-(15)/(x^4)

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\frac{d}{d x} (\frac{5}{x ^{3}} - \frac{2}{x ^{2}} - \frac{1}{x} + 200)

\frac{4}{x ^{3}} + \frac{1}{x ^{2}} - \frac{15}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{5}{x ^{3}} - \frac{2}{x ^{2}} - \frac{1}{x} + 200)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{5}{x ^{3}}) - \frac{d}{d x} (\frac{2}{x ^{2}}) - \frac{d}{d x} (\frac{1}{x}) + \frac{d}{d x} (200)

\frac{d}{d x} (\frac{5}{x ^{3}}) = - \frac{15}{x ^{4}}

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

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

\frac{d}{d x} (200) = 0

= - \frac{15}{x ^{4}} - (- \frac{4}{x ^{3}}) - (- \frac{1}{x ^{2}}) + 0

Simplify

= \frac{4}{x ^{3}} + \frac{1}{x ^{2}} - \frac{15}{x ^{4}}

y = - 2 x^{- 4} + \frac{4}{x} - \frac{2 x ^{2}}{3}

\frac{d}{d x} (x^{2} + 4 x + 4)

\int x 3^{x} d x

\frac{d}{d x} (\frac{csc ( x )}{cot ( x )})

\int \frac{2 x ^{4} - 8 x ^{3} - 6 x ^{2} + 4}{x ^{3}} d x

What is the derivative of 5/(x^3-2/(x^2)-1/x+200) ?
The derivative of 5/(x^3-2/(x^2)-1/x+200) is 4/(x^3)+1/(x^2)-(15)/(x^4)
What is the first derivative of 5/(x^3-2/(x^2)-1/x+200) ?
The first derivative of 5/(x^3-2/(x^2)-1/x+200) is 4/(x^3)+1/(x^2)-(15)/(x^4)