What is the derivative of (x^2-2x-1((x+1)/(x+3))) ?

The derivative of (x^2-2x-1((x+1)/(x+3))) is (2x^3+8x^2-6x-8)/((x+3)^2)

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

The first derivative of (x^2-2x-1((x+1)/(x+3))) is (2x^3+8x^2-6x-8)/((x+3)^2)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} - 2 x - 1, g = \frac{x + 1}{x + 3}

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

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

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

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

Simplify

(2 x - 2) \frac{x + 1}{x + 3} + \frac{2}{( x + 3 ) ^{2}} (x^{2} - 2 x - 1) : \frac{2 x ^{3} + 8 x ^{2} - 6 x - 8}{( x + 3 ) ^{2}}

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

\int \frac{1}{( 4 - x ) ^{2}} d x

(y) d x - (x + y^{2} - x^{2}) d y = 0

\int \frac{54}{1 - cos ( 9 x )} d x

(2 x)^{^{'}}

(ln (cos (x)))^{^{'}}

What is the derivative of (x^2-2x-1((x+1)/(x+3))) ?
The derivative of (x^2-2x-1((x+1)/(x+3))) is (2x^3+8x^2-6x-8)/((x+3)^2)
What is the first derivative of (x^2-2x-1((x+1)/(x+3))) ?
The first derivative of (x^2-2x-1((x+1)/(x+3))) is (2x^3+8x^2-6x-8)/((x+3)^2)