What is (\partial)/(\partial x)(4x^2*3x^3y^2) ?

The answer to (\partial)/(\partial x)(4x^2*3x^3y^2) is 60x^4y^2

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(\partial)/(\partial x)(4x^2*3x^3y^2)

\frac{\partial}{\partial x} (4 x^{2} \cdot 3 x^{3} y^{2})

60 x^{4} y^{2}

Solution steps

\frac{\partial}{\partial x} (4 x^{2} \cdot 3 x^{3} y^{2})

Simplify

4 x^{2} \cdot 3 x^{3} y^{2} : 12 x^{5} y^{2}

= \frac{\partial}{\partial x} (12 x^{5} y^{2})

Treat

y

as a constant

Take the constant out:

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

= 12 y^{2} \frac{\partial}{\partial x} (x^{5})

Apply the Power Rule:

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

= 12 y^{2} \cdot 5 x^{5 - 1}

Simplify

= 60 x^{4} y^{2}

5 x + 1

x \to 0 + lim ((3 x)^{x})

\frac{d}{d x} (- 2 \cdot x)

x \to (\frac{π}{2}) + lim (sec (x))

n = 0 \sum \infty \frac{n}{e ^{n}}

What is (\partial)/(\partial x)(4x^2*3x^3y^2) ?
The answer to (\partial)/(\partial x)(4x^2*3x^3y^2) is 60x^4y^2