What is the derivative of y= 4/x+sqrt(x+0.5)-5x ?

The derivative of y= 4/x+sqrt(x+0.5)-5x is -4/(x^2)+(0.5)/(sqrt(x+0.5))-5

What is the first derivative of y= 4/x+sqrt(x+0.5)-5x ?

The first derivative of y= 4/x+sqrt(x+0.5)-5x is -4/(x^2)+(0.5)/(sqrt(x+0.5))-5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = \frac{4}{x} + x + 0.5 - 5 x

- \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

Solution steps

\frac{d}{d x} (\frac{4}{x} + x + 0.5 - 5 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (x + 0.5) - \frac{d}{d x} (5 x)

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

\frac{d}{d x} (x + 0.5) = \frac{0.5}{x + 0.5}

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

= - \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

What is the derivative of y= 4/x+sqrt(x+0.5)-5x ?
The derivative of y= 4/x+sqrt(x+0.5)-5x is -4/(x^2)+(0.5)/(sqrt(x+0.5))-5
What is the first derivative of y= 4/x+sqrt(x+0.5)-5x ?
The first derivative of y= 4/x+sqrt(x+0.5)-5x is -4/(x^2)+(0.5)/(sqrt(x+0.5))-5