What is (\partial)/(\partial x)(z*log_{e}(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(z*log_{e}(x^2+y^2)) is (2zx)/(x^2+y^2)

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(\partial)/(\partial x)(z*log_{e}(x^2+y^2))

\frac{\partial}{\partial x} (z \cdot lo g_{e} (x^{2} + y^{2}))

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

Solution steps

\frac{\partial}{\partial x} (z lo g_{e} (x^{2} + y^{2}))

Simplify

z lo g_{e} (x^{2} + y^{2}) : z ln (x^{2} + y^{2})

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

d er i v a t i v e ln (e^{2 x})

\int \frac{1}{a} d a

s im pl i f y \frac{4 x ^{3} + 3 x ^{2}}{x}

x \to 1 lim (3 \cdot a + x)

\int \frac{1}{( 121 + x ^{2} ) ^{\frac{3}{2}}} d x

What is (\partial)/(\partial x)(z*log_{e}(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(z*log_{e}(x^2+y^2)) is (2zx)/(x^2+y^2)