What is the derivative of f(x)=(x-3)/(x+3) ?

The derivative of f(x)=(x-3)/(x+3) is 6/((x+3)^2)

What is the first derivative of f(x)=(x-3)/(x+3) ?

The first derivative of f(x)=(x-3)/(x+3) is 6/((x+3)^2)

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derivative of

f (x) = \frac{x - 3}{x + 3}

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

Solution steps

\frac{d}{d x} (\frac{x - 3}{x + 3})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 3) = 1

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

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

Simplify

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

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

\frac{\partial}{\partial y} (\frac{x}{5 + y})

x \to - 1 lim (x - 1)

\frac{d ^{2}}{d t ^{2}} x + 5 \frac{d}{d t} x + 2 x = 0

\frac{\partial}{\partial y} (ln (x^{3} + y^{2}) - ln (x y))

x \to 0 lim (\frac{7 ^{x} - 2 ^{x}}{x})

What is the derivative of f(x)=(x-3)/(x+3) ?
The derivative of f(x)=(x-3)/(x+3) is 6/((x+3)^2)
What is the first derivative of f(x)=(x-3)/(x+3) ?
The first derivative of f(x)=(x-3)/(x+3) is 6/((x+3)^2)