What is the derivative of f(x)=(x-7)/(-5x-10) ?

The derivative of f(x)=(x-7)/(-5x-10) is -9/(5(x+2)^2)

What is the first derivative of f(x)=(x-7)/(-5x-10) ?

The first derivative of f(x)=(x-7)/(-5x-10) is -9/(5(x+2)^2)

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derivative of

f (x) = \frac{x - 7}{- 5 x - 10}

- \frac{9}{5 ( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 7}{- 5 x - 10})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 7 ) ( - 5 x - 10 ) - \frac{d}{d x} ( - 5 x - 10 ) ( x - 7 )}{( - 5 x - 10 ) ^{2}}

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

\frac{d}{d x} (- 5 x - 10) = - 5

= \frac{1 \cdot ( - 5 x - 10 ) - ( - 5 ) ( x - 7 )}{( - 5 x - 10 ) ^{2}}

Simplify

\frac{1 \cdot ( - 5 x - 10 ) - ( - 5 ) ( x - 7 )}{( - 5 x - 10 ) ^{2}} : - \frac{9}{5 ( x + 2 ) ^{2}}

= - \frac{9}{5 ( x + 2 ) ^{2}}

\frac{d}{d x} (13 x^{2} - 5 x + 8)

7 y^{^{'}} + 1 y = 8 e^{3} x, y (0) = 9

f (x) = sin (3 x) cos (5 x)

\frac{1}{1 + 4 x}

\frac{d}{d t} (\frac{t + π}{t} cos (t))

What is the derivative of f(x)=(x-7)/(-5x-10) ?
The derivative of f(x)=(x-7)/(-5x-10) is -9/(5(x+2)^2)
What is the first derivative of f(x)=(x-7)/(-5x-10) ?
The first derivative of f(x)=(x-7)/(-5x-10) is -9/(5(x+2)^2)