What is the derivative of 7-4/(x-8+(2x)/(3x+1)) ?

The derivative of 7-4/(x-8+(2x)/(3x+1)) is (38x^2-8x+132)/((x-8)^2(3x+1)^2)

What is the first derivative of 7-4/(x-8+(2x)/(3x+1)) ?

The first derivative of 7-4/(x-8+(2x)/(3x+1)) is (38x^2-8x+132)/((x-8)^2(3x+1)^2)

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\frac{d}{d x} (7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1})

\frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1})

Simplify

7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1} : \frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )} + 7

= \frac{d}{d x} (\frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )} + 7)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )}) + \frac{d}{d x} (7)

\frac{d}{d x} (\frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )}) = \frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}}

\frac{d}{d x} (7) = 0

= \frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}} + 0

Simplify

= \frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}}

What is the derivative of 7-4/(x-8+(2x)/(3x+1)) ?
The derivative of 7-4/(x-8+(2x)/(3x+1)) is (38x^2-8x+132)/((x-8)^2(3x+1)^2)
What is the first derivative of 7-4/(x-8+(2x)/(3x+1)) ?
The first derivative of 7-4/(x-8+(2x)/(3x+1)) is (38x^2-8x+132)/((x-8)^2(3x+1)^2)