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

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

Popular >

(\partial)/(\partial y)((3x)/(2y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{3 x}{2} (- 1 \cdot y^{- 1 - 1})

Simplify

\frac{3 x}{2} (- 1 \cdot y^{- 1 - 1}) : - \frac{3 x}{2 y ^{2}}

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

\int_{- \infty}^{\infty} 1 d x

\int 5 t \cdot sin^{2} (t) d t

\frac{d}{d x} (arctan (e^{3 x}))

x \to 5 lim (\frac{2}{x - 5})

\frac{d}{d x} (tan (sin (x)))

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