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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{1}{5 - 8 x - x ^{2}} d x

\int (e^{3 x} + e^{- 3 x})^{2} d x

\frac{d}{d x} (ln (4 - 3 x^{3}))

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

t \cdot y^{^{'}} + 2 \cdot y = t^{2} - t + 1

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