What is the derivative of 5/3 x^2y^{-2} ?

The derivative of 5/3 x^2y^{-2} is 5/3 ((2x)/(y^2)-(2x^2\frac{dy)/(dx)}{y^3})

What is the first derivative of 5/3 x^2y^{-2} ?

The first derivative of 5/3 x^2y^{-2} is 5/3 ((2x)/(y^2)-(2x^2\frac{dy)/(dx)}{y^3})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{5}{3} x^{2} y^{- 2})

\frac{5}{3} (\frac{2 x}{y ^{2}} - \frac{2 x ^{2} \frac{d y}{d x}}{y ^{3}})

Solution steps

\frac{d}{d x} (\frac{5}{3} x^{2} y^{- 2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{5}{3} \frac{d}{d x} (x^{2} y^{- 2})

Apply the Product Rule:

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

f = x^{2}, g = y^{- 2}

= \frac{5}{3} (\frac{d}{d x} (x^{2}) y^{- 2} + \frac{d}{d x} (y^{- 2}) x^{2})

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

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

= \frac{5}{3} (2 x y^{- 2} + (- \frac{2 \frac{d y}{d x}}{y ^{3}}) x^{2})

Simplify

\frac{5}{3} (2 x y^{- 2} + (- \frac{2 \frac{d y}{d x}}{y ^{3}}) x^{2}) : \frac{5}{3} (\frac{2 x}{y ^{2}} - \frac{2 x ^{2} \frac{d y}{d x}}{y ^{3}})

= \frac{5}{3} (\frac{2 x}{y ^{2}} - \frac{2 x ^{2} \frac{d y}{d x}}{y ^{3}})

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

n = 0 \sum \infty \frac{n}{1 + n ^{2}}

f (x) = \frac{2}{x ^{2}}, (7, \frac{2}{49})

\frac{d}{d x} (ln (3 x^{2} + 1))

\frac{d}{d y} (\frac{y}{y + \frac{b}{y}})

What is the derivative of 5/3 x^2y^{-2} ?
The derivative of 5/3 x^2y^{-2} is 5/3 ((2x)/(y^2)-(2x^2\frac{dy)/(dx)}{y^3})
What is the first derivative of 5/3 x^2y^{-2} ?
The first derivative of 5/3 x^2y^{-2} is 5/3 ((2x)/(y^2)-(2x^2\frac{dy)/(dx)}{y^3})