What is (\partial)/(\partial x)(6y^2sqrt(x)) ?

The answer to (\partial)/(\partial x)(6y^2sqrt(x)) is (3y^2)/(sqrt(x))

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(\partial)/(\partial x)(6y^2sqrt(x))

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

\frac{3 y ^{2}}{x}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

= 6 y^{2} \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 6 y^{2} \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

6 y^{2} \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3 y ^{2}}{x}

= \frac{3 y ^{2}}{x}

(x x)^{^{'}}

\frac{d y}{d t} + 7 y = e^{4 t}, y (0) = 10

\frac{\partial}{\partial x} (e^{- a x^{2}})

(x + 4)^{2} y^{^{'}} + 3 (x + 4) y = 4

\int \frac{50}{( x - 1 ) ( x ^{2} + 49 )} d x

What is (\partial)/(\partial x)(6y^2sqrt(x)) ?
The answer to (\partial)/(\partial x)(6y^2sqrt(x)) is (3y^2)/(sqrt(x))