What is the derivative of y=(6x)/(x+2) ?

The derivative of y=(6x)/(x+2) is (12)/((x+2)^2)

What is the first derivative of y=(6x)/(x+2) ?

The first derivative of y=(6x)/(x+2) is (12)/((x+2)^2)

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derivative of

y = \frac{6 x}{x + 2}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

e^{- t}

\int \frac{1}{u ^{3}} d u

\frac{\partial}{\partial x} (x^{7} + 3^{y} + x^{y})

\frac{d}{d y} (- ln (y))

\int - \frac{cos ( 2 x )}{2} d x

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