What is (\partial)/(\partial x)(x^{0.1}y^{0.9}) ?

The answer to (\partial)/(\partial x)(x^{0.1}y^{0.9}) is (0.1y^{0.9})/(x^{0.9)}

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(\partial)/(\partial x)(x^{0.1}y^{0.9})

\frac{\partial}{\partial x} (x^{0.1} y^{0.9})

\frac{0.1 y ^{0.9}}{x ^{0.9}}

Solution steps

\frac{\partial}{\partial x} (x^{0.1} y^{0.9})

Treat

y

as a constant

Take the constant out:

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

= y^{0.9} \frac{\partial}{\partial x} (x^{0.1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y^{0.9} \cdot 0.1 x^{0.1 - 1}

Simplify

y^{0.9} \cdot 0.1 x^{0.1 - 1} : \frac{0.1 y ^{0.9}}{x ^{0.9}}

= \frac{0.1 y ^{0.9}}{x ^{0.9}}

x \to 0 lim (\frac{sin ( 4 x ^{2} )}{x})

\frac{\partial}{\partial x} (x \cdot y^{2} \cdot z^{3})

(4 x - 3)^{5} (3 - x^{3})^{2}

y^{^{''}} - 16 y^{^{'}} + 64 y = t^{- 2} e^{8 t}

3 x^{2} + 5 y = 0

What is (\partial)/(\partial x)(x^{0.1}y^{0.9}) ?
The answer to (\partial)/(\partial x)(x^{0.1}y^{0.9}) is (0.1y^{0.9})/(x^{0.9)}