What is the derivative of (3+8x/(5-6x)) ?

The derivative of (3+8x/(5-6x)) is (58)/((5-6x)^2)

What is the first derivative of (3+8x/(5-6x)) ?

The first derivative of (3+8x/(5-6x)) is (58)/((5-6x)^2)

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\frac{d}{d x} (\frac{3 + 8 x}{5 - 6 x})

\frac{58}{( 5 - 6 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 8 x}{5 - 6 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 + 8 x ) ( 5 - 6 x ) - \frac{d}{d x} ( 5 - 6 x ) ( 3 + 8 x )}{( 5 - 6 x ) ^{2}}

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

\frac{d}{d x} (5 - 6 x) = - 6

= \frac{8 ( 5 - 6 x ) - ( - 6 ) ( 3 + 8 x )}{( 5 - 6 x ) ^{2}}

Simplify

\frac{8 ( 5 - 6 x ) - ( - 6 ) ( 3 + 8 x )}{( 5 - 6 x ) ^{2}} : \frac{58}{( 5 - 6 x ) ^{2}}

= \frac{58}{( 5 - 6 x ) ^{2}}

\int (\frac{4}{x}) d x

x \to 1 + lim ((ln (x))^{x - 1})

\frac{d}{d x} (8 x^{3} - 108 x^{2} + 480 x)

x \to 0 lim ((0.5)^{x})

y^{'} = y^{2}

What is the derivative of (3+8x/(5-6x)) ?
The derivative of (3+8x/(5-6x)) is (58)/((5-6x)^2)
What is the first derivative of (3+8x/(5-6x)) ?
The first derivative of (3+8x/(5-6x)) is (58)/((5-6x)^2)