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

The derivative of y=(5/x+x)(5/x-x) is -2x-(50)/(x^3)

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

The first derivative of y=(5/x+x)(5/x-x) is -2x-(50)/(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (\frac{5}{x} + x) (\frac{5}{x} - x)

- 2 x - \frac{50}{x ^{3}}

Solution steps

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

Apply the Product Rule:

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

f = \frac{5}{x} + x, g = \frac{5}{x} - x

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

\frac{d}{d x} (\frac{5}{x} + x) = - \frac{5}{x ^{2}} + 1

\frac{d}{d x} (\frac{5}{x} - x) = - \frac{5}{x ^{2}} - 1

= (- \frac{5}{x ^{2}} + 1) (\frac{5}{x} - x) + (- \frac{5}{x ^{2}} - 1) (\frac{5}{x} + x)

Simplify

(- \frac{5}{x ^{2}} + 1) (\frac{5}{x} - x) + (- \frac{5}{x ^{2}} - 1) (\frac{5}{x} + x) : - 2 x - \frac{50}{x ^{3}}

= - 2 x - \frac{50}{x ^{3}}

y^{^{''}} + y^{^{'}} - 2 = e^{- t}

\int \frac{y ^{2} + 14 y + 49}{( y ^{2} + 49 ) ^{2}} d y

y^{^{'}} + (1 + 3 x^{2}) y = 3 + 9 x^{2}

\int \frac{1 + 2 t ^{3}}{t} d t

\frac{\partial}{\partial x} (2 e^{2 x})

What is the derivative of y=(5/x+x)(5/x-x) ?
The derivative of y=(5/x+x)(5/x-x) is -2x-(50)/(x^3)
What is the first derivative of y=(5/x+x)(5/x-x) ?
The first derivative of y=(5/x+x)(5/x-x) is -2x-(50)/(x^3)