What is (\partial)/(\partial x)(ln(xy^4)) ?

The answer to (\partial)/(\partial x)(ln(xy^4)) is 1/x

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(\partial)/(\partial x)(ln(xy^4))

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

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{x y ^{4}} y^{4}

Simplify

\frac{1}{x y ^{4}} y^{4} : \frac{1}{x}

= \frac{1}{x}

y = 3 x e^{2 x}

\int - 1120 (1 + 4 t)^{- 3} d t

f (x) = 5 x^{2} - x^{3}

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

\int \frac{x}{( x ^{2} - 1 ) [ ln ( x ^{2} - 1 ) ] ^{2}} d x

What is (\partial)/(\partial x)(ln(xy^4)) ?
The answer to (\partial)/(\partial x)(ln(xy^4)) is 1/x