What is the derivative of f(x)=(1-5x)/(1+5x) ?

The derivative of f(x)=(1-5x)/(1+5x) is -(10)/((1+5x)^2)

What is the first derivative of f(x)=(1-5x)/(1+5x) ?

The first derivative of f(x)=(1-5x)/(1+5x) is -(10)/((1+5x)^2)

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derivative of

f (x) = \frac{1 - 5 x}{1 + 5 x}

- \frac{10}{( 1 + 5 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 5 x}{1 + 5 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 5 x ) ( 1 + 5 x ) - \frac{d}{d x} ( 1 + 5 x ) ( 1 - 5 x )}{( 1 + 5 x ) ^{2}}

\frac{d}{d x} (1 - 5 x) = - 5

\frac{d}{d x} (1 + 5 x) = 5

= \frac{( - 5 ) ( 1 + 5 x ) - 5 ( 1 - 5 x )}{( 1 + 5 x ) ^{2}}

Simplify

\frac{( - 5 ) ( 1 + 5 x ) - 5 ( 1 - 5 x )}{( 1 + 5 x ) ^{2}} : - \frac{10}{( 1 + 5 x ) ^{2}}

= - \frac{10}{( 1 + 5 x ) ^{2}}

1 - e^{- x}

\frac{1}{e ^{x}}

\frac{d}{d x} (5 x^{5})

x \to 0 lim (cot (x) - csc (x))

f (x) = \frac{1}{x - 5}

What is the derivative of f(x)=(1-5x)/(1+5x) ?
The derivative of f(x)=(1-5x)/(1+5x) is -(10)/((1+5x)^2)
What is the first derivative of f(x)=(1-5x)/(1+5x) ?
The first derivative of f(x)=(1-5x)/(1+5x) is -(10)/((1+5x)^2)