What is the derivative of (1/(x^2-3/(x^4))*(x+5x^3)) ?

The derivative of (1/(x^2-3/(x^4))*(x+5x^3)) is (14)/(x^2)+9/(x^4)+5

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

The first derivative of (1/(x^2-3/(x^4))*(x+5x^3)) is (14)/(x^2)+9/(x^4)+5

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

\frac{14}{x ^{2}} + \frac{9}{x ^{4}} + 5

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x ^{2}} - \frac{3}{x ^{4}}, g = x + 5 x^{3}

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

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

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

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

Simplify

(- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 5 x^{3}) + (1 + 15 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) : \frac{14}{x ^{2}} + \frac{9}{x ^{4}} + 5

= \frac{14}{x ^{2}} + \frac{9}{x ^{4}} + 5

What is the derivative of (1/(x^2-3/(x^4))*(x+5x^3)) ?
The derivative of (1/(x^2-3/(x^4))*(x+5x^3)) is (14)/(x^2)+9/(x^4)+5
What is the first derivative of (1/(x^2-3/(x^4))*(x+5x^3)) ?
The first derivative of (1/(x^2-3/(x^4))*(x+5x^3)) is (14)/(x^2)+9/(x^4)+5