What is (\partial)/(\partial x)(u/(1+2.4(x/y))) ?

The answer to (\partial)/(\partial x)(u/(1+2.4(x/y))) is -(2.4uy)/((y+2.4x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(u/(1+2.4(x/y)))

\frac{\partial}{\partial x} \frac{u}{1 + 2.4 ( \frac{x}{y} )}

- \frac{2.4 u y}{( y + 2.4 x ) ^{2}}

Solution steps

\frac{\partial}{\partial x} \frac{u}{1 + 2.4 ( \frac{x}{y} )}

Treat

u, y

as constants

Take the constant out:

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

= u \frac{\partial}{\partial x} (\frac{1}{1 + 2.4 \cdot \frac{x}{y}})

Apply exponent rule:

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

= u \frac{\partial}{\partial x} ((1 + 2.4 \cdot \frac{x}{y})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 2.4 \cdot \frac{x}{y} ) ^{2}} \frac{\partial}{\partial x} (1 + 2.4 \cdot \frac{x}{y})

= - \frac{1}{( 1 + 2.4 \cdot \frac{x}{y} ) ^{2}} \frac{\partial}{\partial x} (1 + 2.4 \cdot \frac{x}{y})

\frac{\partial}{\partial x} (1 + 2.4 \cdot \frac{x}{y}) = \frac{2.4}{y}

= u - \frac{1}{( 1 + 2.4 \cdot \frac{x}{y} ) ^{2}} \cdot \frac{2.4}{y}

Simplify

u - \frac{1}{( 1 + 2.4 \cdot \frac{x}{y} ) ^{2}} \cdot \frac{2.4}{y} : - \frac{2.4 u y}{( y + 2.4 x ) ^{2}}

= - \frac{2.4 u y}{( y + 2.4 x ) ^{2}}

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 5 x^{4} y^{7})

\int_{0}^{3} 15 x d x

x \to 0 lim (x (x))

x \to - 2 lim (\frac{x ^{2} - 6}{2 - x})

\frac{1}{s ^{3} + s ^{2}}

What is (\partial)/(\partial x)(u/(1+2.4(x/y))) ?
The answer to (\partial)/(\partial x)(u/(1+2.4(x/y))) is -(2.4uy)/((y+2.4x)^2)