What is the derivative of (5x+6)/(4x+2) ?

The derivative of (5x+6)/(4x+2) is -7/(2(2x+1)^2)

What is the first derivative of (5x+6)/(4x+2) ?

The first derivative of (5x+6)/(4x+2) is -7/(2(2x+1)^2)

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derivative of

\frac{5 x + 6}{4 x + 2}

- \frac{7}{2 ( 2 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x + 6}{4 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 + 6 ) ( 4 x + 2 ) - \frac{d}{d x} ( 4 x + 2 ) ( 5 x + 6 )}{( 4 x + 2 ) ^{2}}

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

\frac{d}{d x} (4 x + 2) = 4

= \frac{5 ( 4 x + 2 ) - 4 ( 5 x + 6 )}{( 4 x + 2 ) ^{2}}

Simplify

\frac{5 ( 4 x + 2 ) - 4 ( 5 x + 6 )}{( 4 x + 2 ) ^{2}} : - \frac{7}{2 ( 2 x + 1 ) ^{2}}

= - \frac{7}{2 ( 2 x + 1 ) ^{2}}

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

\int (sec^{2} (θ) + 6) d θ

1 - 2 sin^{2} (x)

y = (\frac{x + 3}{x - 1})^{2}, (5, 4)

f (x) = sin (x) + arcsin (x)

What is the derivative of (5x+6)/(4x+2) ?
The derivative of (5x+6)/(4x+2) is -7/(2(2x+1)^2)
What is the first derivative of (5x+6)/(4x+2) ?
The first derivative of (5x+6)/(4x+2) is -7/(2(2x+1)^2)