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

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

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

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

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

- \frac{3}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= - \frac{3}{x ^{4}}

n \to \infty lim (- 2^{n})

n \to \infty lim (n - 3)

y = 3 + 4 x^{2} - 2 x^{3}, at x = 1

n = 0 \sum \infty \frac{2 n}{n !}

\int (e^{9 x} + 7 e^{- x}) d x

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