What is (\partial)/(\partial x)(x^{3/4}y^3) ?

The answer to (\partial)/(\partial x)(x^{3/4}y^3) is (3y^3)/(4x^{1/4)}

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(\partial)/(\partial x)(x^{3/4}y^3)

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

\frac{3 y ^{3}}{4 x ^{\frac{1}{4}}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= y^{3} \frac{3}{4} x^{\frac{3}{4} - 1}

Simplify

y^{3} \frac{3}{4} x^{\frac{3}{4} - 1} : \frac{3 y ^{3}}{4 x ^{\frac{1}{4}}}

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

\frac{d}{d x} ((x^{4} + x - 7) (2 x^{3} + 1))

x \to 0 - lim (x^{2} - 2 ln (x))

\int 4 x^{2} - 1 d x

x^{2} + 2 x + 2, 3 x + 8, [0, 2]

x \to 2 lim (x^{2} + 5)

What is (\partial)/(\partial x)(x^{3/4}y^3) ?
The answer to (\partial)/(\partial x)(x^{3/4}y^3) is (3y^3)/(4x^{1/4)}