What is (\partial)/(\partial x)(5x^2y^5) ?

The answer to (\partial)/(\partial x)(5x^2y^5) is 10xy^5

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(\partial)/(\partial x)(5x^2y^5)

\frac{\partial}{\partial x} (5 x^{2} y^{5})

10 x y^{5}

Solution steps

\frac{\partial}{\partial x} (5 x^{2} y^{5})

Treat

y

as a constant

Take the constant out:

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

= 5 y^{5} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

= 5 y^{5} \cdot 2 x^{2 - 1}

Simplify

= 10 x y^{5}

\frac{\partial}{\partial y} (x y^{6} + x^{2} + y^{4})

\frac{\partial}{\partial z} (arctan (\frac{x}{z}))

- 2 x^{2} + 50 x + 25.247

\frac{d}{d x} (x^{3} + 10)

\int \frac{ln ( x + 1 )}{( x + 1 ) ^{3}} d x

What is (\partial)/(\partial x)(5x^2y^5) ?
The answer to (\partial)/(\partial x)(5x^2y^5) is 10xy^5