What is (\partial)/(\partial y)(x^3ln(y^5)) ?

The answer to (\partial)/(\partial y)(x^3ln(y^5)) is (5x^3)/y

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(\partial)/(\partial y)(x^3ln(y^5))

\frac{\partial}{\partial y} (x^{3} ln (y^{5}))

\frac{5 x ^{3}}{y}

Solution steps

\frac{\partial}{\partial y} (x^{3} ln (y^{5}))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x^{3} \frac{\partial}{\partial y} (ln (y^{5}))

Apply the chain rule:

\frac{1}{y ^{5}} \frac{\partial}{\partial y} (y^{5})

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

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

= x^{3} \frac{1}{y ^{5}} \cdot 5 y^{4}

Simplify

x^{3} \frac{1}{y ^{5}} \cdot 5 y^{4} : \frac{5 x ^{3}}{y}

= \frac{5 x ^{3}}{y}

\frac{1}{( s + 4 ) ^{3}}

x^{2} \frac{d y}{d x} - 2 x y = 6 y^{4}

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

\int \frac{6}{25 - x ^{2}} d x

t^{2} y^{^{''}} - 2 t y^{^{'}} + 2 y = 3 t^{2} - t^{3}

What is (\partial)/(\partial y)(x^3ln(y^5)) ?
The answer to (\partial)/(\partial y)(x^3ln(y^5)) is (5x^3)/y