What is the derivative of f(x)=(6x)/(x+5) ?

The derivative of f(x)=(6x)/(x+5) is (30)/((x+5)^2)

What is the first derivative of f(x)=(6x)/(x+5) ?

The first derivative of f(x)=(6x)/(x+5) is (30)/((x+5)^2)

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derivative of

f (x) = \frac{6 x}{x + 5}

\frac{30}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x}{x + 5})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{x}{x + 5})

Apply the Quotient Rule:

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

= 6 \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

= 6 \cdot \frac{1 \cdot ( x + 5 ) - 1 \cdot x}{( x + 5 ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( x + 5 ) - 1 \cdot x}{( x + 5 ) ^{2}} : \frac{30}{( x + 5 ) ^{2}}

= \frac{30}{( x + 5 ) ^{2}}

8 x e^{- k x}

n = 1 \sum \infty \frac{2 ^{n}}{( n ) !}

\frac{d}{d x} (x^{2} + 9 x)

\frac{\partial}{\partial x} (e^{x^{2} - y^{2}} (cos (2 x y) + sin (2 x y)))

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What is the derivative of f(x)=(6x)/(x+5) ?
The derivative of f(x)=(6x)/(x+5) is (30)/((x+5)^2)
What is the first derivative of f(x)=(6x)/(x+5) ?
The first derivative of f(x)=(6x)/(x+5) is (30)/((x+5)^2)