What is the derivative of 6/(3x^5+2/(5x^2)-7/(9x)) ?

The derivative of 6/(3x^5+2/(5x^2)-7/(9x)) is -(10)/(x^6)-4/(5x^3)+7/(9x^2)

What is the first derivative of 6/(3x^5+2/(5x^2)-7/(9x)) ?

The first derivative of 6/(3x^5+2/(5x^2)-7/(9x)) is -(10)/(x^6)-4/(5x^3)+7/(9x^2)

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\frac{d}{d x} (\frac{6}{3 x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x})

- \frac{10}{x ^{6}} - \frac{4}{5 x ^{3}} + \frac{7}{9 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{6}{3 x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x})

Simplify

\frac{6}{3 x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x} : \frac{2}{x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x}

= \frac{d}{d x} (\frac{2}{x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{2}{x ^{5}}) + \frac{d}{d x} (\frac{2}{5 x ^{2}}) - \frac{d}{d x} (\frac{7}{9 x})

\frac{d}{d x} (\frac{2}{x ^{5}}) = - \frac{10}{x ^{6}}

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

\frac{d}{d x} (\frac{7}{9 x}) = - \frac{7}{9 x ^{2}}

= - \frac{10}{x ^{6}} - \frac{4}{5 x ^{3}} - (- \frac{7}{9 x ^{2}})

Simplify

= - \frac{10}{x ^{6}} - \frac{4}{5 x ^{3}} + \frac{7}{9 x ^{2}}

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

y^{^{''}} - 4 y^{^{'}} - 12 y = 8 e^{- 2 x}

\frac{d}{d x} (x e^{x} cos (x))

\int (5 x^{2} + 2 x^{3}) d x

x (\frac{d y}{d x}) = x tan (\frac{y}{x}) + y

What is the derivative of 6/(3x^5+2/(5x^2)-7/(9x)) ?
The derivative of 6/(3x^5+2/(5x^2)-7/(9x)) is -(10)/(x^6)-4/(5x^3)+7/(9x^2)
What is the first derivative of 6/(3x^5+2/(5x^2)-7/(9x)) ?
The first derivative of 6/(3x^5+2/(5x^2)-7/(9x)) is -(10)/(x^6)-4/(5x^3)+7/(9x^2)