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}}

\int e^{x} (x^{2} - 2 x + 2) d x

arctan (x^{4})

y = \frac{1}{x + 1} + 1

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

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- x} sec (2 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)