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

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

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

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

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derivative of

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

\frac{3 x ^{2} + 3 x - 2}{2 x x}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{3 x ^{2} + 3 x - 2}{2 x x}

x \to - 3 + lim (\frac{- 5 x}{x + 3})

\int_{0}^{1} x 3^{x} d x

2 x d y + y d x = 0

x y y^{^{'}} + 4 x^{2} + y^{2} = 0

2 x d z - 2 z d x = x^{2} + 4 z^{2} d x

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