What is the derivative of (5x^2-9x+8/(7x+2)) ?

The derivative of (5x^2-9x+8/(7x+2)) is (35x^2+20x-74)/((7x+2)^2)

What is the first derivative of (5x^2-9x+8/(7x+2)) ?

The first derivative of (5x^2-9x+8/(7x+2)) is (35x^2+20x-74)/((7x+2)^2)

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\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 8}{7 x + 2})

\frac{35 x ^{2} + 20 x - 74}{( 7 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 8}{7 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} - 9 x + 8 ) ( 7 x + 2 ) - \frac{d}{d x} ( 7 x + 2 ) ( 5 x ^{2} - 9 x + 8 )}{( 7 x + 2 ) ^{2}}

\frac{d}{d x} (5 x^{2} - 9 x + 8) = 10 x - 9

\frac{d}{d x} (7 x + 2) = 7

= \frac{( 10 x - 9 ) ( 7 x + 2 ) - 7 ( 5 x ^{2} - 9 x + 8 )}{( 7 x + 2 ) ^{2}}

Expand

(10 x - 9) (7 x + 2) - 7 (5 x^{2} - 9 x + 8) : 35 x^{2} + 20 x - 74

= \frac{35 x ^{2} + 20 x - 74}{( 7 x + 2 ) ^{2}}

y = x^{3} - 3 x^{2} - x + 3, - 1 < x < 3

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3})

\frac{d}{d x} (\frac{3 x ^{4}}{tan ( x )})

5^{2 x}

\frac{d}{d x} (\frac{q x + r}{s x + r})

What is the derivative of (5x^2-9x+8/(7x+2)) ?
The derivative of (5x^2-9x+8/(7x+2)) is (35x^2+20x-74)/((7x+2)^2)
What is the first derivative of (5x^2-9x+8/(7x+2)) ?
The first derivative of (5x^2-9x+8/(7x+2)) is (35x^2+20x-74)/((7x+2)^2)