What is (\partial)/(\partial x)(ln(x^5-y^4)) ?

The answer to (\partial)/(\partial x)(ln(x^5-y^4)) is (5x^4)/(x^5-y^4)

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(\partial)/(\partial x)(ln(x^5-y^4))

\frac{\partial}{\partial x} (ln (x^{5} - y^{4}))

\frac{5 x ^{4}}{x ^{5} - y ^{4}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{5} - y^{4}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{5} - y ^{4}} \frac{\partial}{\partial x} (x^{5} - y^{4})

= \frac{1}{x ^{5} - y ^{4}} \frac{\partial}{\partial x} (x^{5} - y^{4})

\frac{\partial}{\partial x} (x^{5} - y^{4}) = 5 x^{4}

= \frac{1}{x ^{5} - y ^{4}} \cdot 5 x^{4}

Simplify

\frac{1}{x ^{5} - y ^{4}} \cdot 5 x^{4} : \frac{5 x ^{4}}{x ^{5} - y ^{4}}

= \frac{5 x ^{4}}{x ^{5} - y ^{4}}

\frac{d}{d x} (a cos (3 x))

(3 x^{2})^{2 x}

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

\int (e^{x} - e^{- x}) d x

\frac{\partial}{\partial u} (u cos (v))

What is (\partial)/(\partial x)(ln(x^5-y^4)) ?
The answer to (\partial)/(\partial x)(ln(x^5-y^4)) is (5x^4)/(x^5-y^4)