What is (\partial)/(\partial x)(ln(x^4+y^9)) ?

The answer to (\partial)/(\partial x)(ln(x^4+y^9)) is (4x^3)/(x^4+y^9)

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(\partial)/(\partial x)(ln(x^4+y^9))

\frac{\partial}{\partial x} (ln (x^{4} + y^{9}))

\frac{4 x ^{3}}{x ^{4} + y ^{9}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{4} + y^{9}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{4} + y ^{9}} \frac{\partial}{\partial x} (x^{4} + y^{9})

= \frac{1}{x ^{4} + y ^{9}} \frac{\partial}{\partial x} (x^{4} + y^{9})

\frac{\partial}{\partial x} (x^{4} + y^{9}) = 4 x^{3}

= \frac{1}{x ^{4} + y ^{9}} \cdot 4 x^{3}

Simplify

\frac{1}{x ^{4} + y ^{9}} \cdot 4 x^{3} : \frac{4 x ^{3}}{x ^{4} + y ^{9}}

= \frac{4 x ^{3}}{x ^{4} + y ^{9}}

\frac{\partial}{\partial x} (x \cdot e^{- y})

\frac{d y}{d x} = 1

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

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

x \to - 2 lim (\frac{3 x + 6}{x + 2})

What is (\partial)/(\partial x)(ln(x^4+y^9)) ?
The answer to (\partial)/(\partial x)(ln(x^4+y^9)) is (4x^3)/(x^4+y^9)