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Popular >

derivative of (3x+8)/(x^2)

Solution

derivative of

\frac{3 x + 8}{x ^{2}}

Solution

\frac{- 3 x - 16}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{3 x + 8}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 8 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x + 8 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x + 8) = 3

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

= \frac{3 x ^{2} - 2 x ( 3 x + 8 )}{( x ^{2} ) ^{2}}

Simplify

\frac{3 x ^{2} - 2 x ( 3 x + 8 )}{( x ^{2} ) ^{2}} : \frac{- 3 x - 16}{x ^{3}}

= \frac{- 3 x - 16}{x ^{3}}

Popular Examples

inverse oflaplace ((3s+1))/(s+2)inverse laplace

\frac{( 3 s + 1 )}{s + 2}

(\partial)/(\partial y)(x/((x+y)^2))

\frac{\partial}{\partial y} (\frac{x}{( x + y ) ^{2}})

integral from 1 to 3 of (x^3+1/(4x^3))

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

normal of y=2x-1+4x^2,(1,5)normal of

y = 2 x - 1 + 4 x^{2}, (1, 5)

integral of ke^{-x}

\int k e^{- x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (3x+8)/(x^2) ?
The derivative of (3x+8)/(x^2) is (-3x-16)/(x^3)
What is the first derivative of (3x+8)/(x^2) ?
The first derivative of (3x+8)/(x^2) is (-3x-16)/(x^3)