What is (\partial)/(\partial x)(x^3y^7) ?

The answer to (\partial)/(\partial x)(x^3y^7) is 3x^2y^7

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(\partial)/(\partial x)(x^3y^7)

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

3 x^{2} y^{7}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= y^{7} \cdot 3 x^{3 - 1}

Simplify

= 3 x^{2} y^{7}

- 5 t^{2} e^{- 4 t} + sin (3 t)

\frac{d}{d x} (x^{3} - 7 x^{2} + 14 x - 6)

\frac{\partial}{\partial u} (\frac{u}{v + 1})

\int g e^{- 2 c t} d t

x \to - 1 lim (\frac{x + 1}{1 - x ^{2}})

What is (\partial)/(\partial x)(x^3y^7) ?
The answer to (\partial)/(\partial x)(x^3y^7) is 3x^2y^7