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

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

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

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

4 x^{3} y^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 4 x^{3} y^{3}

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

\int_{- 4}^{6} 6 d x

f (x) = - 4 x^{2} - 4 x + 4, at x = 1

- \frac{12}{( 4 x + 1 ) ^{2}}

\int \frac{1}{( e ^{y} + 1 ) ^{2} e ^{- y}} d y

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