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

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

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

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

4 x^{3} y^{3}

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

\int (\frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}) d y

\int_{1}^{5} \frac{1}{( 5 - x ) ^{\frac{5}{2}}} d x

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

f (x) = (4 x + 5)^{3} (x^{2} - 6 x + 5)^{4}

\int \frac{36}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

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