What is (\partial)/(\partial x)((4sqrt(x))/(3y^2+1)) ?

The answer to (\partial)/(\partial x)((4sqrt(x))/(3y^2+1)) is 2/(sqrt(x)(3y^2+1))

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(\partial)/(\partial x)((4sqrt(x))/(3y^2+1))

\frac{\partial}{\partial x} (\frac{4 x}{3 y ^{2} + 1})

\frac{2}{x ( 3 y ^{2} + 1 )}

Solution steps

\frac{\partial}{\partial x} (\frac{4 x}{3 y ^{2} + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{4}{3 y ^{2} + 1} \frac{\partial}{\partial x} (x)

Apply radical rule:

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

= \frac{4}{3 y ^{2} + 1} \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= \frac{4}{3 y ^{2} + 1} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

\frac{4}{3 y ^{2} + 1} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{2}{x ( 3 y ^{2} + 1 )}

= \frac{2}{x ( 3 y ^{2} + 1 )}

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

\int e^{11 x} (11) d x

\int x^{3} tan (x y) d y

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

- y + x \frac{d y}{d x} ln (x) = 0

What is (\partial)/(\partial x)((4sqrt(x))/(3y^2+1)) ?
The answer to (\partial)/(\partial x)((4sqrt(x))/(3y^2+1)) is 2/(sqrt(x)(3y^2+1))