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

The answer to (\partial)/(\partial x)(ln(x^3+y^7)) is (3x^2)/(x^3+y^7)

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

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

\frac{3 x ^{2}}{x ^{3} + y ^{7}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{3} + y^{7}) = 3 x^{2}

= \frac{1}{x ^{3} + y ^{7}} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} + y ^{7}} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + y ^{7}}

= \frac{3 x ^{2}}{x ^{3} + y ^{7}}

\frac{d}{d x} (sin^{- 5} (x) - cos^{3} (x))

\int \frac{( x + 1 )}{x} d x

(csc^{2} (x))^{^{'}}

\int \frac{x}{25 - x ^{2}} d x

\frac{d y}{d x}, y^{3} = x^{2}

What is (\partial)/(\partial x)(ln(x^3+y^7)) ?
The answer to (\partial)/(\partial x)(ln(x^3+y^7)) is (3x^2)/(x^3+y^7)