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

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

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

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

\frac{2}{4 x + y ^{3}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{1}{x})

\frac{d y}{d x} = \frac{1}{2} y + x

d er i v a t i v e f (x) = \frac{10 x}{1 - x}

t a y l or cos (x) e^{x}

y^{^{''}} = - a

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