What is (\partial)/(\partial x)(ln(x^7-y^6)) ?

The answer to (\partial)/(\partial x)(ln(x^7-y^6)) is (7x^6)/(x^7-y^6)

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(\partial)/(\partial x)(ln(x^7-y^6))

\frac{\partial}{\partial x} (ln (x^{7} - y^{6}))

\frac{7 x ^{6}}{x ^{7} - y ^{6}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{7} - y^{6}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{7} - y ^{6}} \frac{\partial}{\partial x} (x^{7} - y^{6})

= \frac{1}{x ^{7} - y ^{6}} \frac{\partial}{\partial x} (x^{7} - y^{6})

\frac{\partial}{\partial x} (x^{7} - y^{6}) = 7 x^{6}

= \frac{1}{x ^{7} - y ^{6}} \cdot 7 x^{6}

Simplify

\frac{1}{x ^{7} - y ^{6}} \cdot 7 x^{6} : \frac{7 x ^{6}}{x ^{7} - y ^{6}}

= \frac{7 x ^{6}}{x ^{7} - y ^{6}}

\int 5 tan^{2} (x) sec (x) d x

\int arctan (1) d x

\frac{d}{d x} ((π - x) cos (x))

2 x^{2} - 4 x - 1

\frac{d}{d x} (e^{∣ x ∣})

What is (\partial)/(\partial x)(ln(x^7-y^6)) ?
The answer to (\partial)/(\partial x)(ln(x^7-y^6)) is (7x^6)/(x^7-y^6)