What is (\partial)/(\partial x)(ln(x^8-y^6)) ?

The answer to (\partial)/(\partial x)(ln(x^8-y^6)) is (8x^7)/(x^8-y^6)

(\partial)/(\partial x)(ln(x^8-y^6))

\frac{\partial}{\partial x} (ln (x^{8} - y^{6}))

\frac{8 x ^{7}}{x ^{8} - y ^{6}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{8} - y^{6}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{8} - y ^{6}} \frac{\partial}{\partial x} (x^{8} - y^{6})

= \frac{1}{x ^{8} - y ^{6}} \frac{\partial}{\partial x} (x^{8} - y^{6})

\frac{\partial}{\partial x} (x^{8} - y^{6}) = 8 x^{7}

= \frac{1}{x ^{8} - y ^{6}} \cdot 8 x^{7}

Simplify

\frac{1}{x ^{8} - y ^{6}} \cdot 8 x^{7} : \frac{8 x ^{7}}{x ^{8} - y ^{6}}

= \frac{8 x ^{7}}{x ^{8} - y ^{6}}

\int e^{x} a^{x} d x

x^{2} y^{^{'}} + y = \frac{x}{y}, y (1) = 4

\frac{( y ^{^{'}} - e - t + 4 )}{y} = - 4

x \to 0 lim (\frac{7 ^{s i n (x)} - 1}{x})

\int \frac{1}{9} x^{- \frac{8}{9}} d x

What is (\partial)/(\partial x)(ln(x^8-y^6)) ?
The answer to (\partial)/(\partial x)(ln(x^8-y^6)) is (8x^7)/(x^8-y^6)