What is the derivative of (1/(x^2)-3/(x^4))(x+9x^3) ?

The derivative of (1/(x^2)-3/(x^4))(x+9x^3) is (26)/(x^2)+9/(x^4)+9

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

The first derivative of (1/(x^2)-3/(x^4))(x+9x^3) is (26)/(x^2)+9/(x^4)+9

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derivative of

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

\frac{26}{x ^{2}} + \frac{9}{x ^{4}} + 9

Solution steps

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) (x + 9 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 + 9 x^{3}

= \frac{d}{d x} (\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) (x + 9 x^{3}) + \frac{d}{d x} (x + 9 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 + 9 x^{3}) = 1 + 27 x^{2}

= (- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 9 x^{3}) + (1 + 27 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}})

Simplify

(- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 9 x^{3}) + (1 + 27 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) : \frac{26}{x ^{2}} + \frac{9}{x ^{4}} + 9

= \frac{26}{x ^{2}} + \frac{9}{x ^{4}} + 9

\int \frac{2}{( 1 + x ^{2} ) ^{2}} d x

\frac{d ^{2} y}{d t ^{2}} + 10 \frac{d y}{d t} + 25 y = 0

\frac{d}{d x} (\frac{x ^{3} y + x y ^{3}}{x ^{2} + y ^{2}})

f (x) = x - 4, (13, 3)

f (x) = \frac{5}{x + 1}, at x = \frac{- 1}{3}

What is the derivative of (1/(x^2)-3/(x^4))(x+9x^3) ?
The derivative of (1/(x^2)-3/(x^4))(x+9x^3) is (26)/(x^2)+9/(x^4)+9
What is the first derivative of (1/(x^2)-3/(x^4))(x+9x^3) ?
The first derivative of (1/(x^2)-3/(x^4))(x+9x^3) is (26)/(x^2)+9/(x^4)+9