What is the derivative of f(x)=(x-3)/(5x+2) ?

The derivative of f(x)=(x-3)/(5x+2) is (17)/((5x+2)^2)

What is the first derivative of f(x)=(x-3)/(5x+2) ?

The first derivative of f(x)=(x-3)/(5x+2) is (17)/((5x+2)^2)

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derivative of

f (x) = \frac{x - 3}{5 x + 2}

\frac{17}{( 5 x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (5 x + 2) = 5

= \frac{1 \cdot ( 5 x + 2 ) - 5 ( x - 3 )}{( 5 x + 2 ) ^{2}}

Simplify

\frac{1 \cdot ( 5 x + 2 ) - 5 ( x - 3 )}{( 5 x + 2 ) ^{2}} : \frac{17}{( 5 x + 2 ) ^{2}}

= \frac{17}{( 5 x + 2 ) ^{2}}

- 4 cos (x), at x = \frac{π}{2}

\int \frac{4 x ^{2}}{x ^{2} + 8} d x

y = (\frac{( x - 1 )}{( x - 2 )})^{2}

\frac{d}{d x} (- csc (x) cot (x))

\frac{d y}{d x} + \frac{e}{π} y = 5

What is the derivative of f(x)=(x-3)/(5x+2) ?
The derivative of f(x)=(x-3)/(5x+2) is (17)/((5x+2)^2)
What is the first derivative of f(x)=(x-3)/(5x+2) ?
The first derivative of f(x)=(x-3)/(5x+2) is (17)/((5x+2)^2)