What is the derivative of y=(2x+5)/(5x^2) ?

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

What is the first derivative of y=(2x+5)/(5x^2) ?

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

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derivative of

y = \frac{2 x + 5}{5 x ^{2}}

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

Solution steps

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

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{2 x + 5}{x ^{2}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

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

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

\int \frac{48 x ^{2}}{( x - 9 ) ( x + 3 ) ^{2}} d x

\frac{d}{d x} (\frac{3 x ^{3} + x}{2 x - 7})

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

\int (x - \frac{1}{2})^{2} d x

\int_{- 5}^{5} x 25 - x^{2} d x

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