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Popular >

derivative of (x+3/(x^2))

Solution

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

Solution

\frac{- x - 6}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 3) = 1

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

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

Simplify

\frac{1 \cdot x ^{2} - 2 x ( x + 3 )}{( x ^{2} ) ^{2}} : \frac{- x - 6}{x ^{3}}

= \frac{- x - 6}{x ^{3}}

Popular Examples

integral from-2 to 1 of (4-x^2)-(x+2)

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

derivative of f(x)=(5x^2-8x)e^x derivative of

f (x) = (5 x^{2} - 8 x) e^{x}

derivative of 3/(sqrt(6x+8))derivative of

\frac{3}{6 x + 8}

area 12-x^2,x^2-6 area

12 - x^{2}, x^{2} - 6

area y=x,y=x^2 area

y = x, y = x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (x+3/(x^2)) ?
The derivative of (x+3/(x^2)) is (-x-6)/(x^3)
What is the first derivative of (x+3/(x^2)) ?
The first derivative of (x+3/(x^2)) is (-x-6)/(x^3)