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_{0}^{π} 3 sin^{4} (3 t) d t

\frac{15}{( s + 10 ) ( s + 11 )}

\int_{0}^{2.8} 0.2 x d x

\frac{4 π r ^{3}}{3}

\frac{x ^{3}}{x + 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