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

The derivative of (5x-3(4x-3/x)) is 40x-9/(x^2)-12

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

The first derivative of (5x-3(4x-3/x)) is 40x-9/(x^2)-12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

40 x - \frac{9}{x ^{2}} - 12

Solution steps

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

Simplify

(5 x - 3) (4 x - \frac{3}{x}) : 20 x^{2} - 15 - 12 x + \frac{9}{x}

= \frac{d}{d x} (20 x^{2} - 15 - 12 x + \frac{9}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (20 x^{2}) - \frac{d}{d x} (15) - \frac{d}{d x} (12 x) + \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (20 x^{2}) = 40 x

\frac{d}{d x} (15) = 0

\frac{d}{d x} (12 x) = 12

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

= 40 x - 0 - 12 - \frac{9}{x ^{2}}

Simplify

= 40 x - \frac{9}{x ^{2}} - 12

\int \frac{x ^{2}}{x ^{3} + 9} d x

\frac{d}{d x} (9 x^{2} e^{x})

\frac{d}{d x} (x sinh (x) - cosh (x))

\int \frac{3 x}{x ^{2} + 5} d x

\int csc^{2} (5 x) d x

What is the derivative of (5x-3(4x-3/x)) ?
The derivative of (5x-3(4x-3/x)) is 40x-9/(x^2)-12
What is the first derivative of (5x-3(4x-3/x)) ?
The first derivative of (5x-3(4x-3/x)) is 40x-9/(x^2)-12