What is (\partial)/(\partial x)(xln(z^3+x^6)) ?

The answer to (\partial)/(\partial x)(xln(z^3+x^6)) is ln(z^3+x^6)+(6x^6)/(z^3+x^6)

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(\partial)/(\partial x)(xln(z^3+x^6))

\frac{\partial}{\partial x} (x ln (z^{3} + x^{6}))

ln (z^{3} + x^{6}) + \frac{6 x ^{6}}{z ^{3} + x ^{6}}

Solution steps

\frac{\partial}{\partial x} (x ln (z^{3} + 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^{3} + x^{6})

= \frac{\partial}{\partial x} (x) ln (z^{3} + x^{6}) + \frac{\partial}{\partial x} (ln (z^{3} + x^{6})) x

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

\frac{\partial}{\partial x} (ln (z^{3} + x^{6})) = \frac{6 x ^{5}}{z ^{3} + x ^{6}}

= 1 \cdot ln (z^{3} + x^{6}) + \frac{6 x ^{5}}{z ^{3} + x ^{6}} x

Simplify

1 \cdot ln (z^{3} + x^{6}) + \frac{6 x ^{5}}{z ^{3} + x ^{6}} x : ln (z^{3} + x^{6}) + \frac{6 x ^{6}}{z ^{3} + x ^{6}}

= ln (z^{3} + x^{6}) + \frac{6 x ^{6}}{z ^{3} + x ^{6}}

y = tan (π - \frac{9}{x})

12 + 2.8 sin (\frac{2 π}{365} (t - 80))

n = 0 \sum \infty \frac{4}{2 ^{n}}

f (x) = cos (x)

(- 18 - 20) (- 18 - 15)

What is (\partial)/(\partial x)(xln(z^3+x^6)) ?
The answer to (\partial)/(\partial x)(xln(z^3+x^6)) is ln(z^3+x^6)+(6x^6)/(z^3+x^6)