What is the derivative of (4x)/(x-5) ?

The derivative of (4x)/(x-5) is -(20)/((x-5)^2)

What is the first derivative of (4x)/(x-5) ?

The first derivative of (4x)/(x-5) is -(20)/((x-5)^2)

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derivative of

\frac{4 x}{x - 5}

- \frac{20}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x}{x - 5})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x}{x - 5})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} ( x - 5 ) - \frac{d}{d x} ( x - 5 ) x}{( x - 5 ) ^{2}}

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

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

= 4 \cdot \frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}} : - \frac{20}{( x - 5 ) ^{2}}

= - \frac{20}{( x - 5 ) ^{2}}

y = tan (\frac{t}{1 + t ^{2}})

\int_{0}^{1} 4 π (x^{2} - x^{10}) d x

\frac{3}{x}

\int 2 x (x^{2} + 5)^{5} d x

\frac{280}{s ^{2} + 14 s + 245}

What is the derivative of (4x)/(x-5) ?
The derivative of (4x)/(x-5) is -(20)/((x-5)^2)
What is the first derivative of (4x)/(x-5) ?
The first derivative of (4x)/(x-5) is -(20)/((x-5)^2)