What is (\partial)/(\partial x)(x^3esqrt(3xy)) ?

The answer to (\partial)/(\partial x)(x^3esqrt(3xy)) is (7sqrt(3)ex^{5/2}sqrt(y))/2

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(\partial)/(\partial x)(x^3esqrt(3xy))

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

\frac{7 3 e x ^{\frac{5}{2}} y}{2}

Solution steps

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

Simplify

x^{3} e 3 x y : 3 e x^{\frac{7}{2}} y

= \frac{\partial}{\partial x} (3 e x^{\frac{7}{2}} y)

Treat

y

as a constant

Take the constant out:

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

= 3 e y \frac{\partial}{\partial x} (x^{\frac{7}{2}})

Apply the Power Rule:

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

= 3 e y \frac{7}{2} x^{\frac{7}{2} - 1}

Simplify

3 e y \frac{7}{2} x^{\frac{7}{2} - 1} : \frac{7 3 e x ^{\frac{5}{2}} y}{2}

= \frac{7 3 e x ^{\frac{5}{2}} y}{2}

\frac{d}{d x} (y^{2} cos (x))

\frac{\partial}{\partial x} (25 + x^{2})

\frac{d y}{d x} - 2 y = x^{2} + 5

2 y \frac{d y}{d x} = \frac{x}{x ^{2} - 16}

\frac{\partial}{\partial x} (4 e^{x y} ln (x^{2} + y^{2}))

What is (\partial)/(\partial x)(x^3esqrt(3xy)) ?
The answer to (\partial)/(\partial x)(x^3esqrt(3xy)) is (7sqrt(3)ex^{5/2}sqrt(y))/2