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

The derivative of (3-sqrt(2x+5))/(x-2) is (x-3sqrt(2x+5)+7)/((x-2)^2sqrt(2x+5))

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

The first derivative of (3-sqrt(2x+5))/(x-2) is (x-3sqrt(2x+5)+7)/((x-2)^2sqrt(2x+5))

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derivative of

\frac{3 - 2 x + 5}{x - 2}

\frac{x - 3 2 x + 5 + 7}{( x - 2 ) ^{2} 2 x + 5}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 2) = 1

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

Simplify

\frac{( - \frac{1}{2 x + 5} ) ( x - 2 ) - 1 \cdot ( 3 - 2 x + 5 )}{( x - 2 ) ^{2}} : \frac{x - 3 2 x + 5 + 7}{( x - 2 ) ^{2} 2 x + 5}

= \frac{x - 3 2 x + 5 + 7}{( x - 2 ) ^{2} 2 x + 5}

x \to 0 lim (x^{2} + 2 x + 1)

t^{2} y^{^{''}} + 3 t y^{^{'}} + y = \frac{1}{t}

\int_{0}^{1} x - x^{2} d x

x \to 0 lim (\frac{1}{3 + x} - \frac{1}{3})

\int 6 + 7 t^{2} d t

What is the derivative of (3-sqrt(2x+5))/(x-2) ?
The derivative of (3-sqrt(2x+5))/(x-2) is (x-3sqrt(2x+5)+7)/((x-2)^2sqrt(2x+5))
What is the first derivative of (3-sqrt(2x+5))/(x-2) ?
The first derivative of (3-sqrt(2x+5))/(x-2) is (x-3sqrt(2x+5)+7)/((x-2)^2sqrt(2x+5))