What is the derivative of (1/(x^2-6/(x^4))(x+8x^3)) ?

The derivative of (1/(x^2-6/(x^4))(x+8x^3)) is (47)/(x^2)+(18)/(x^4)+8

What is the first derivative of (1/(x^2-6/(x^4))(x+8x^3)) ?

The first derivative of (1/(x^2-6/(x^4))(x+8x^3)) is (47)/(x^2)+(18)/(x^4)+8

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\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) (x + 8 x^{3}))

\frac{47}{x ^{2}} + \frac{18}{x ^{4}} + 8

Solution steps

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) (x + 8 x^{3}))

Apply the Product Rule:

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

f = \frac{1}{x ^{2}} - \frac{6}{x ^{4}}, g = x + 8 x^{3}

= \frac{d}{d x} (\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) (x + 8 x^{3}) + \frac{d}{d x} (x + 8 x^{3}) (\frac{1}{x ^{2}} - \frac{6}{x ^{4}})

\frac{d}{d x} (\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) = - \frac{2}{x ^{3}} + \frac{24}{x ^{5}}

\frac{d}{d x} (x + 8 x^{3}) = 1 + 24 x^{2}

= (- \frac{2}{x ^{3}} + \frac{24}{x ^{5}}) (x + 8 x^{3}) + (1 + 24 x^{2}) (\frac{1}{x ^{2}} - \frac{6}{x ^{4}})

Simplify

(- \frac{2}{x ^{3}} + \frac{24}{x ^{5}}) (x + 8 x^{3}) + (1 + 24 x^{2}) (\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) : \frac{47}{x ^{2}} + \frac{18}{x ^{4}} + 8

= \frac{47}{x ^{2}} + \frac{18}{x ^{4}} + 8

x \to 1 lim (\frac{0}{x ^{2} - 1})

\int (18 x + 5) d x

\int 2 e^{3 x} d x

3 x \cdot \frac{d y}{d x} - y = x

\frac{d}{d x} (e^{x} \frac{1}{x})

What is the derivative of (1/(x^2-6/(x^4))(x+8x^3)) ?
The derivative of (1/(x^2-6/(x^4))(x+8x^3)) is (47)/(x^2)+(18)/(x^4)+8
What is the first derivative of (1/(x^2-6/(x^4))(x+8x^3)) ?
The first derivative of (1/(x^2-6/(x^4))(x+8x^3)) is (47)/(x^2)+(18)/(x^4)+8