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

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

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

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

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\frac{d}{d 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{\partial}{\partial x} (x y + y z^{2} + x z^{3})

\frac{\partial}{\partial x} ((x + z) e^{x - y})

\int \frac{1}{( 6 x - 1 ) ^{2}} d x

\frac{d}{d x} (- 16 x^{2})

\frac{\partial}{\partial z} (9 z e^{x yz})

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