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}}

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\frac{\partial}{\partial x} (3 x + 5 y)

\frac{d}{d x} (\frac{x}{4 + x ^{2}})

x \to 0 lim (\frac{sin ( 9 x )}{sin ( 3 x )})

\int - 4 e^{x} sin (4 y) d y

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)