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Popular >

derivative of (x^2+3/x)

Solution

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

Solution

\frac{x ^{2} - 3}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x ^{2} - 3}{x ^{2}}

Popular Examples

derivative of y=x^2sin^6(x)+xcos^{-2}(x)derivative of

y = x^{2} sin^{6} (x) + x cos^{- 2} (x)

limit as x approaches 4 of (3x-9)^4

x \to 4 lim ((3 x - 9)^{4})

derivative of y=sqrt(x+7)derivative of

y = x + 7

(dy)/(dx)=(1+4y^2)(1+3x^2)

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

limit as x approaches 0 of (sin(7x))/(sin(9x))

x \to 0 lim (\frac{sin ( 7 x )}{sin ( 9 x )})

Frequently Asked Questions (FAQ)

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