What is the derivative of (x^2-7x+10/(3x^2-15x)) ?

The derivative of (x^2-7x+10/(3x^2-15x)) is 2/(3x^2)

What is the first derivative of (x^2-7x+10/(3x^2-15x)) ?

The first derivative of (x^2-7x+10/(3x^2-15x)) is 2/(3x^2)

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\frac{d}{d x} (\frac{x ^{2} - 7 x + 10}{3 x ^{2} - 15 x})

\frac{2}{3 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 7 x + 10}{3 x ^{2} - 15 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 7 x + 10 ) ( 3 x ^{2} - 15 x ) - \frac{d}{d x} ( 3 x ^{2} - 15 x ) ( x ^{2} - 7 x + 10 )}{( 3 x ^{2} - 15 x ) ^{2}}

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

\frac{d}{d x} (3 x^{2} - 15 x) = 6 x - 15

= \frac{( 2 x - 7 ) ( 3 x ^{2} - 15 x ) - ( 6 x - 15 ) ( x ^{2} - 7 x + 10 )}{( 3 x ^{2} - 15 x ) ^{2}}

Simplify

\frac{( 2 x - 7 ) ( 3 x ^{2} - 15 x ) - ( 6 x - 15 ) ( x ^{2} - 7 x + 10 )}{( 3 x ^{2} - 15 x ) ^{2}} : \frac{2}{3 x ^{2}}

= \frac{2}{3 x ^{2}}

f (x) = \frac{2 x + 5}{5 x - 1}, at x = - 1

\int \frac{x ^{2} + 6 x}{x ^{3} - x ^{2} + x - 1} d x

x \to 2 lim ((x + 1) \cdot (x + 3))

\frac{\partial}{\partial x} (x e^{- x} (a + b x + c x^{2}))

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x y^{3})

What is the derivative of (x^2-7x+10/(3x^2-15x)) ?
The derivative of (x^2-7x+10/(3x^2-15x)) is 2/(3x^2)
What is the first derivative of (x^2-7x+10/(3x^2-15x)) ?
The first derivative of (x^2-7x+10/(3x^2-15x)) is 2/(3x^2)