What is (\partial)/(\partial x)(xln(z^4+x^6)) ?

The answer to (\partial)/(\partial x)(xln(z^4+x^6)) is ln(z^4+x^6)+(6x^6)/(z^4+x^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xln(z^4+x^6))

\frac{\partial}{\partial x} (x ln (z^{4} + x^{6}))

ln (z^{4} + x^{6}) + \frac{6 x ^{6}}{z ^{4} + x ^{6}}

Solution steps

\frac{\partial}{\partial x} (x ln (z^{4} + x^{6}))

Treat

z

as a constant

Apply the Product Rule:

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

f = x, g = ln (z^{4} + x^{6})

= \frac{\partial}{\partial x} (x) ln (z^{4} + x^{6}) + \frac{\partial}{\partial x} (ln (z^{4} + x^{6})) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (z^{4} + x^{6})) = \frac{6 x ^{5}}{z ^{4} + x ^{6}}

= 1 \cdot ln (z^{4} + x^{6}) + \frac{6 x ^{5}}{z ^{4} + x ^{6}} x

Simplify

1 \cdot ln (z^{4} + x^{6}) + \frac{6 x ^{5}}{z ^{4} + x ^{6}} x : ln (z^{4} + x^{6}) + \frac{6 x ^{6}}{z ^{4} + x ^{6}}

= ln (z^{4} + x^{6}) + \frac{6 x ^{6}}{z ^{4} + x ^{6}}

f (x) = 3 x - 1

\frac{d ^{4}}{d x ^{4}} (19 e^{x^{2}})

\frac{d}{d x} (x a^{2} - x^{2})

\int \frac{1}{- x ^{2} - 10 x - 24} d x

x \to 3 lim (1 - x - x^{2})

What is (\partial)/(\partial x)(xln(z^4+x^6)) ?
The answer to (\partial)/(\partial x)(xln(z^4+x^6)) is ln(z^4+x^6)+(6x^6)/(z^4+x^6)