What is the derivative of y=(5x-3)((4x-3)/x) ?

The derivative of y=(5x-3)((4x-3)/x) is (20x^2-9)/(x^2)

What is the first derivative of y=(5x-3)((4x-3)/x) ?

The first derivative of y=(5x-3)((4x-3)/x) is (20x^2-9)/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = (5 x - 3) (\frac{4 x - 3}{x})

\frac{20 x ^{2} - 9}{x ^{2}}

Solution steps

\frac{d}{d x} ((5 x - 3) \frac{4 x - 3}{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 5 x - 3, g = \frac{4 x - 3}{x}

= \frac{d}{d x} (5 x - 3) \frac{4 x - 3}{x} + \frac{d}{d x} (\frac{4 x - 3}{x}) (5 x - 3)

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

\frac{d}{d x} (\frac{4 x - 3}{x}) = \frac{3}{x ^{2}}

= 5 \cdot \frac{4 x - 3}{x} + \frac{3}{x ^{2}} (5 x - 3)

Simplify

5 \cdot \frac{4 x - 3}{x} + \frac{3}{x ^{2}} (5 x - 3) : \frac{20 x ^{2} - 9}{x ^{2}}

= \frac{20 x ^{2} - 9}{x ^{2}}

\frac{- 5}{( 4 x - 2 y + 2 )}

y = 5 x^{8} - 6 x + 12

f (t) = 3 + 8 t - t^{2}

y = x^{2} + 5

20 q - 2 q^{2}

What is the derivative of y=(5x-3)((4x-3)/x) ?
The derivative of y=(5x-3)((4x-3)/x) is (20x^2-9)/(x^2)
What is the first derivative of y=(5x-3)((4x-3)/x) ?
The first derivative of y=(5x-3)((4x-3)/x) is (20x^2-9)/(x^2)