What is the derivative of f(x)=(x^2-1)/x ?

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

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

\int ln (x^{2} + 3) d x

\int \frac{1}{n ln ( n )}

\int_{- 1}^{3} (- x^{3} + 2 x - 11) d x

t^{3} e^{t}

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