What is the derivative of (1+6x/(9-4x)) ?

The derivative of (1+6x/(9-4x)) is (58)/((9-4x)^2)

What is the first derivative of (1+6x/(9-4x)) ?

The first derivative of (1+6x/(9-4x)) is (58)/((9-4x)^2)

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\frac{d}{d x} (\frac{1 + 6 x}{9 - 4 x})

\frac{58}{( 9 - 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 + 6 x}{9 - 4 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 + 6 x ) ( 9 - 4 x ) - \frac{d}{d x} ( 9 - 4 x ) ( 1 + 6 x )}{( 9 - 4 x ) ^{2}}

\frac{d}{d x} (1 + 6 x) = 6

\frac{d}{d x} (9 - 4 x) = - 4

= \frac{6 ( 9 - 4 x ) - ( - 4 ) ( 1 + 6 x )}{( 9 - 4 x ) ^{2}}

Simplify

\frac{6 ( 9 - 4 x ) - ( - 4 ) ( 1 + 6 x )}{( 9 - 4 x ) ^{2}} : \frac{58}{( 9 - 4 x ) ^{2}}

= \frac{58}{( 9 - 4 x ) ^{2}}

y^{2} - 2 x = 7, x - y = 4

x^{5} \cdot e^{x}

y = ∣ x - 12 ∣, y = \frac{x}{3}

f (x) = x^{3} - x^{2} + 3

(1 + x)^{\frac{1}{2}}

What is the derivative of (1+6x/(9-4x)) ?
The derivative of (1+6x/(9-4x)) is (58)/((9-4x)^2)
What is the first derivative of (1+6x/(9-4x)) ?
The first derivative of (1+6x/(9-4x)) is (58)/((9-4x)^2)