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

The derivative of (z(z/(z+2)+1)) is (x^2+4x)/((x+2)^2)+1

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

The first derivative of (z(z/(z+2)+1)) is (x^2+4x)/((x+2)^2)+1

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

\frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} + 1

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot (\frac{x}{x + 2} + 1) + \frac{2}{( x + 2 ) ^{2}} x : \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} + 1

= \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} + 1

- \frac{l k ( l sin ( \frac{2 π x}{l} ) + 2 C π )}{4 π ^{2}}

3 (y - 40 = - 38)

f (∣ x ∣ - 1) e^{∣ x ∣}

1 - x ((- 2 - x) (4 - x))

\frac{[ x ( x - 1 ) - 2 ]}{2}

What is the derivative of (z(z/(z+2)+1)) ?
The derivative of (z(z/(z+2)+1)) is (x^2+4x)/((x+2)^2)+1
What is the first derivative of (z(z/(z+2)+1)) ?
The first derivative of (z(z/(z+2)+1)) is (x^2+4x)/((x+2)^2)+1