What is the derivative of (a-x)/(a+x) ?

The derivative of (a-x)/(a+x) is -(2a)/((a+x)^2)

What is the first derivative of (a-x)/(a+x) ?

The first derivative of (a-x)/(a+x) is -(2a)/((a+x)^2)

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derivative of

\frac{a - x}{a + x}

- \frac{2 a}{( a + x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 2 lim (x^{2} + 2 x)

x \to 0 + lim \frac{1}{4 x ^{\frac{6}{7}}} - \frac{7}{( x - 6 ^{\frac{6}{7}} )}

\frac{12}{x ^{5}}

\frac{9 - sec ( x )}{tan ( x )}

\frac{\partial}{\partial t} (\frac{3 r + s}{t})

What is the derivative of (a-x)/(a+x) ?
The derivative of (a-x)/(a+x) is -(2a)/((a+x)^2)
What is the first derivative of (a-x)/(a+x) ?
The first derivative of (a-x)/(a+x) is -(2a)/((a+x)^2)