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

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

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

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

\frac{1}{2 x + y ^{4}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d x} ((2 x^{3} + 3 x - 1)^{4})

\frac{\partial}{\partial x} (3 x^{3} y^{3} - 2 x^{2} + 3 y + 40)

2 - \frac{4}{t}

\int \frac{ln ( 13 x )}{x} d x

e^{3 x}

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