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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to + (- 1) lim (\frac{sin ( x )}{x})

\frac{d y}{d x} = y^{3}

f (x) = \frac{x}{9 - x}

n = 1 \sum \infty (- \frac{1}{3})^{n - 1}

x^{3} x^{3} + 3

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