What is the derivative of ((7x-1(x+5))/(36x)) ?

The derivative of ((7x-1(x+5))/(36x)) is (7x^2+5)/(36x^2)

What is the first derivative of ((7x-1(x+5))/(36x)) ?

The first derivative of ((7x-1(x+5))/(36x)) is (7x^2+5)/(36x^2)

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\frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{36 x})

\frac{7 x ^{2} + 5}{36 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{36 x})

Take the constant out:

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

= \frac{1}{36} \frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{x})

Apply the Quotient Rule:

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

= \frac{1}{36} \cdot \frac{\frac{d}{d x} ( ( 7 x - 1 ) ( x + 5 ) ) x - \frac{d x}{d x} ( 7 x - 1 ) ( x + 5 )}{x ^{2}}

\frac{d}{d x} ((7 x - 1) (x + 5)) = 14 x + 34

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

= \frac{1}{36} \cdot \frac{( 14 x + 34 ) x - 1 \cdot ( 7 x - 1 ) ( x + 5 )}{x ^{2}}

Simplify

\frac{1}{36} \cdot \frac{( 14 x + 34 ) x - 1 \cdot ( 7 x - 1 ) ( x + 5 )}{x ^{2}} : \frac{7 x ^{2} + 5}{36 x ^{2}}

= \frac{7 x ^{2} + 5}{36 x ^{2}}

What is the derivative of ((7x-1(x+5))/(36x)) ?
The derivative of ((7x-1(x+5))/(36x)) is (7x^2+5)/(36x^2)
What is the first derivative of ((7x-1(x+5))/(36x)) ?
The first derivative of ((7x-1(x+5))/(36x)) is (7x^2+5)/(36x^2)