What is the derivative of y=(x^2+x+1)/x ?

The derivative of y=(x^2+x+1)/x is (x^2-1)/(x^2)

What is the first derivative of y=(x^2+x+1)/x ?

The first derivative of y=(x^2+x+1)/x is (x^2-1)/(x^2)

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derivative of

y = \frac{x ^{2} + x + 1}{x}

\frac{x ^{2} - 1}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= \frac{x ^{2} - 1}{x ^{2}}

y = x^{4}

y = sin (2 x)

4 x + 2 y = 6

cos (2 x)

(- 1.5) (5.5)

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