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Popular >

derivative of (x^2+x+1/x)

Solution

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

Solution

\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}}

Popular Examples

y^{^{''}} + 9 y = 0

tangent of y=10cot((pix)/(20)),\at x=5 tangent of

y = 10 cot (\frac{π x}{20}), at x = 5

derivative of (3+x{f}(x)/(sqrt(x)))

\frac{d}{d x} (\frac{3 + x f ( x )}{x})

derivative of (arctan(4x))^2 derivative of

(arctan (4 x))^{2}

2(d^2y)/(dx^2)+8y=cos(2x)

2 \frac{d ^{2} y}{d x ^{2}} + 8 y = cos (2 x)

Frequently Asked Questions (FAQ)

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