What is (\partial)/(\partial x)(-(7x^2)/(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(-(7x^2)/(x^2+y^2)) is -(14xy^2)/((x^2+y^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(-(7x^2)/(x^2+y^2))

\frac{\partial}{\partial x} (- \frac{7 x ^{2}}{x ^{2} + y ^{2}})

- \frac{14 x y ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (- \frac{7 x ^{2}}{x ^{2} + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= - 7 \frac{\partial}{\partial x} (\frac{x ^{2}}{x ^{2} + y ^{2}})

Apply the Quotient Rule:

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

= - 7 \cdot \frac{\frac{\partial}{\partial x} ( x ^{2} ) ( x ^{2} + y ^{2} ) - \frac{\partial}{\partial x} ( x ^{2} + y ^{2} ) x ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

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

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

= - 7 \cdot \frac{2 x ( x ^{2} + y ^{2} ) - 2 x x ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

Simplify

- 7 \cdot \frac{2 x ( x ^{2} + y ^{2} ) - 2 x x ^{2}}{( x ^{2} + y ^{2} ) ^{2}} : - \frac{14 x y ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

= - \frac{14 x y ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

5 - \frac{4}{x ^{2}}, at x = 4

x \to \infty lim (x^{3})

\frac{2 s}{s ^{2} + 6 s + 9}

\int_{1}^{e^{8}} \frac{ln ^{2} ( x ^{2} )}{x} d x

4 x^{2} - x, 1, 3

What is (\partial)/(\partial x)(-(7x^2)/(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(-(7x^2)/(x^2+y^2)) is -(14xy^2)/((x^2+y^2)^2)