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

The derivative of (5x/(1-x)) is 5/((1-x)^2)

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

The first derivative of (5x/(1-x)) is 5/((1-x)^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (2 x sin (2 x))

y^{^{''}} + 2 y^{^{'}} + 10 y = cos (t) + 0.739

f (x) = 11 x^{3} tan (x)

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{x})

\int \frac{1}{y ^{2} - y} d y

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