What is (\partial)/(\partial x)(3x^4y^5) ?

The answer to (\partial)/(\partial x)(3x^4y^5) is 12x^3y^5

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(\partial)/(\partial x)(3x^4y^5)

\frac{\partial}{\partial x} (3 x^{4} y^{5})

12 x^{3} y^{5}

Solution steps

\frac{\partial}{\partial x} (3 x^{4} y^{5})

Treat

y

as a constant

Take the constant out:

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

= 3 y^{5} \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

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

= 3 y^{5} \cdot 4 x^{4 - 1}

Simplify

= 12 x^{3} y^{5}

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

\int cos (x) - cos^{3} (x) d x

f (x) = 7 + x^{2}

7 e^{7 e^{x} + x}

f (z) = 3 x + 2 z + 4 x z

What is (\partial)/(\partial x)(3x^4y^5) ?
The answer to (\partial)/(\partial x)(3x^4y^5) is 12x^3y^5