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

The derivative of f(x)=(6x)/(x+6) is (36)/((x+6)^2)

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

The first derivative of f(x)=(6x)/(x+6) is (36)/((x+6)^2)

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derivative of

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

\frac{36}{( x + 6 ) ^{2}}

Solution steps

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

Take the constant out:

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

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

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

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

\frac{d}{d x} (x + 6) = 1

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

Simplify

6 \cdot \frac{1 \cdot ( x + 6 ) - 1 \cdot x}{( x + 6 ) ^{2}} : \frac{36}{( x + 6 ) ^{2}}

= \frac{36}{( x + 6 ) ^{2}}

\frac{d}{d x} (ln (3 x^{2} + 5))

36 y^{^{''}} - 12 y^{^{'}} + y = 0

x \to 0 + lim (x^{2} - ln (x))

\frac{d}{d x} ((x - 4)^{3})

f (x) = \frac{lo g _{9} ( x )}{7 + x ^{9}}

What is the derivative of f(x)=(6x)/(x+6) ?
The derivative of f(x)=(6x)/(x+6) is (36)/((x+6)^2)
What is the first derivative of f(x)=(6x)/(x+6) ?
The first derivative of f(x)=(6x)/(x+6) is (36)/((x+6)^2)