What is (\partial)/(\partial y)((y-t)/(5y+2t)) ?

The answer to (\partial)/(\partial y)((y-t)/(5y+2t)) is (7t)/((5y+2t)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)((y-t)/(5y+2t))

\frac{\partial}{\partial y} (\frac{y - t}{5 y + 2 t})

\frac{7 t}{( 5 y + 2 t ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{y - t}{5 y + 2 t})

Treat

t

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{\partial}{\partial y} (y - t) = 1

\frac{\partial}{\partial y} (5 y + 2 t) = 5

= \frac{1 \cdot ( 5 y + 2 t ) - 5 ( y - t )}{( 5 y + 2 t ) ^{2}}

Simplify

\frac{1 \cdot ( 5 y + 2 t ) - 5 ( y - t )}{( 5 y + 2 t ) ^{2}} : \frac{7 t}{( 5 y + 2 t ) ^{2}}

= \frac{7 t}{( 5 y + 2 t ) ^{2}}

t - π

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

\frac{d}{d x} (ln (x^{2} - 4))

\frac{d}{d t} (e^{5 t s i n (2 t)})

\frac{d}{d x} (e^{l n (x)})

What is (\partial)/(\partial y)((y-t)/(5y+2t)) ?
The answer to (\partial)/(\partial y)((y-t)/(5y+2t)) is (7t)/((5y+2t)^2)