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

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

Popular >

(\partial)/(\partial x)(ln(x^2+y^2+3))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{x ^{2} + y ^{2} + 3} \cdot 2 x

Simplify

\frac{1}{x ^{2} + y ^{2} + 3} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{2} + 3}

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

4 sin (x)

\frac{5}{s + 5}

\frac{2 s + 1}{s ^{2} + 2 s + 10}

\int \frac{8}{5 t 25 t ^{2} - 25} d t

\frac{d}{d x} (\frac{x ^{2} - 2 x - 3}{x + 2})

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