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

The answer to (\partial)/(\partial x)(x^2ln(x^2+y^2)) is 2xln(x^2+y^2)+(2x^3)/(x^2+y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x^2ln(x^2+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = ln (x^{2} + y^{2})

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

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

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

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

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

= 2 x ln (x^{2} + y^{2}) + \frac{2 x ^{3}}{x ^{2} + y ^{2}}

\int (7 x^{6} + 7 x^{3} + 4) d x

\int e^{l n (x^{2})} x d x

\frac{d}{d x} (e^{2 x} - cos (2 x))

x \to 0 lim (\frac{( sin ( 4 x ) )}{x})

\int - 3 sin (5 x) cos^{2} (5 x) d x

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