What is (\partial)/(\partial x)(ln(x^7-y^3)) ?

The answer to (\partial)/(\partial x)(ln(x^7-y^3)) is (7x^6)/(x^7-y^3)

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(\partial)/(\partial x)(ln(x^7-y^3))

\frac{\partial}{\partial x} (ln (x^{7} - y^{3}))

\frac{7 x ^{6}}{x ^{7} - y ^{3}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{7} - y^{3}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{7} - y ^{3}} \frac{\partial}{\partial x} (x^{7} - y^{3})

= \frac{1}{x ^{7} - y ^{3}} \frac{\partial}{\partial x} (x^{7} - y^{3})

\frac{\partial}{\partial x} (x^{7} - y^{3}) = 7 x^{6}

= \frac{1}{x ^{7} - y ^{3}} \cdot 7 x^{6}

Simplify

\frac{1}{x ^{7} - y ^{3}} \cdot 7 x^{6} : \frac{7 x ^{6}}{x ^{7} - y ^{3}}

= \frac{7 x ^{6}}{x ^{7} - y ^{3}}

f (x) = e^{\frac{a}{x}}

\int \frac{- 2 x ^{4}}{( 1 - x ) ^{3}} d x

sin (x^{3})

f (t) = 2 t

What is (\partial)/(\partial x)(ln(x^7-y^3)) ?
The answer to (\partial)/(\partial x)(ln(x^7-y^3)) is (7x^6)/(x^7-y^3)