What is (\partial)/(\partial x)((3y^2)/((5x+3y)^2)) ?

The answer to (\partial)/(\partial x)((3y^2)/((5x+3y)^2)) is -(30y^2)/((5x+3y)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((3y^2)/((5x+3y)^2))

\frac{\partial}{\partial x} (\frac{3 y ^{2}}{( 5 x + 3 y ) ^{2}})

- \frac{30 y ^{2}}{( 5 x + 3 y ) ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{3 y ^{2}}{( 5 x + 3 y ) ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 3 y^{2} \frac{\partial}{\partial x} (\frac{1}{( 5 x + 3 y ) ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (5 x + 3 y) = 5

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

Simplify

3 y^{2} (- \frac{2}{( 5 x + 3 y ) ^{3}} \cdot 5) : - \frac{30 y ^{2}}{( 5 x + 3 y ) ^{3}}

= - \frac{30 y ^{2}}{( 5 x + 3 y ) ^{3}}

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

\int \frac{1}{x} - x^{2} + sin (x) - 3^{x} d x

\frac{d y}{d x} + 2 y = 9 e^{x}

\frac{\partial}{\partial y} (3 x + 8 y + 2)

\frac{\partial}{\partial x} (y ln (y))

What is (\partial)/(\partial x)((3y^2)/((5x+3y)^2)) ?
The answer to (\partial)/(\partial x)((3y^2)/((5x+3y)^2)) is -(30y^2)/((5x+3y)^3)