What is the derivative of f(x)= x/(3x+8) ?

The derivative of f(x)= x/(3x+8) is 8/((3x+8)^2)

What is the first derivative of f(x)= x/(3x+8) ?

The first derivative of f(x)= x/(3x+8) is 8/((3x+8)^2)

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derivative of

f (x) = \frac{x}{3 x + 8}

\frac{8}{( 3 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{3 x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 3 x + 8 ) - \frac{d}{d x} ( 3 x + 8 ) x}{( 3 x + 8 ) ^{2}}

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

\frac{d}{d x} (3 x + 8) = 3

= \frac{1 \cdot ( 3 x + 8 ) - 3 x}{( 3 x + 8 ) ^{2}}

Simplify

= \frac{8}{( 3 x + 8 ) ^{2}}

x \to - 1 lim (\frac{x ^{2} - 1}{x - 3})

\int \frac{ln ( x + 1 )}{2 ( x + 1 )} d x

\int 8 x^{- 2} d x

\frac{d}{d x} (tan^{4} (2 x - 1)^{3})

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

What is the derivative of f(x)= x/(3x+8) ?
The derivative of f(x)= x/(3x+8) is 8/((3x+8)^2)
What is the first derivative of f(x)= x/(3x+8) ?
The first derivative of f(x)= x/(3x+8) is 8/((3x+8)^2)