What is the derivative of (6x/(6+sqrt(x))) ?

The derivative of (6x/(6+sqrt(x))) is (3(sqrt(x)+12))/((6+sqrt(x))^2)

What is the first derivative of (6x/(6+sqrt(x))) ?

The first derivative of (6x/(6+sqrt(x))) is (3(sqrt(x)+12))/((6+sqrt(x))^2)

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\frac{d}{d x} (\frac{6 x}{6 + x})

\frac{3 ( x + 12 )}{( 6 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x}{6 + x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{x}{6 + x})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d x}{d x} ( 6 + x ) - \frac{d}{d x} ( 6 + x ) x}{( 6 + x ) ^{2}}

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

\frac{d}{d x} (6 + x) = \frac{1}{2 x}

= 6 \cdot \frac{1 \cdot ( 6 + x ) - \frac{1}{2 x} x}{( 6 + x ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( 6 + x ) - \frac{1}{2 x} x}{( 6 + x ) ^{2}} : \frac{3 ( x + 12 )}{( 6 + x ) ^{2}}

= \frac{3 ( x + 12 )}{( 6 + x ) ^{2}}

\frac{\partial}{\partial x} (\frac{( x + y )}{y})

y = - 0.0959 x^{2} + 106.83 x + 71149

\int 2 e^{t x} x d x

\int_{1}^{R} x^{- \frac{9}{5}} d x

What is the derivative of (6x/(6+sqrt(x))) ?
The derivative of (6x/(6+sqrt(x))) is (3(sqrt(x)+12))/((6+sqrt(x))^2)
What is the first derivative of (6x/(6+sqrt(x))) ?
The first derivative of (6x/(6+sqrt(x))) is (3(sqrt(x)+12))/((6+sqrt(x))^2)