What is the derivative of ((x^2)/(5+8x)) ?

The derivative of ((x^2)/(5+8x)) is (10x+8x^2)/((5+8x)^2)

What is the first derivative of ((x^2)/(5+8x)) ?

The first derivative of ((x^2)/(5+8x)) is (10x+8x^2)/((5+8x)^2)

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\frac{d}{d x} (\frac{( x ^{2} )}{5 + 8 x})

\frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} )}{5 + 8 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 5 + 8 x ) - \frac{d}{d x} ( 5 + 8 x ) x ^{2}}{( 5 + 8 x ) ^{2}}

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

\frac{d}{d x} (5 + 8 x) = 8

= \frac{2 x ( 5 + 8 x ) - 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Expand

2 x (5 + 8 x) - 8 x^{2} : 10 x + 8 x^{2}

= \frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

\frac{d}{d x} (\frac{20}{x ^{6}})

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 12 e^{x}

n = 1 \sum \infty \frac{5 + n}{n !}

y^{^{'}} + 100 y = 0

n = 1 \sum \infty 2^{n} \cdot 3^{- n}

What is the derivative of ((x^2)/(5+8x)) ?
The derivative of ((x^2)/(5+8x)) is (10x+8x^2)/((5+8x)^2)
What is the first derivative of ((x^2)/(5+8x)) ?
The first derivative of ((x^2)/(5+8x)) is (10x+8x^2)/((5+8x)^2)