What is (\partial)/(\partial x)(ln(x^4+y^3)) ?

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

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(\partial)/(\partial x)(ln(x^4+y^3))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{4} + y ^{3}} \frac{\partial}{\partial x} (x^{4} + y^{3})

= \frac{1}{x ^{4} + y ^{3}} \frac{\partial}{\partial x} (x^{4} + y^{3})

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

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

Simplify

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

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

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

x \to 1 lim (2 x - x^{2} - x^{3})

\frac{\partial}{\partial x} (2 x^{2} - 4)

\frac{\partial}{\partial x} (1 + x y)

(5.12) (- 3.4)

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