What is (\partial)/(\partial x)(sqrt(2x+y^{10)}) ?

The answer to (\partial)/(\partial x)(sqrt(2x+y^{10)}) is 1/(sqrt(2x+y^{10))}

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(\partial)/(\partial x)(sqrt(2x+y^{10)})

\frac{\partial}{\partial x} (2 x + y^{10})

\frac{1}{2 x + y ^{10}}

Solution steps

\frac{\partial}{\partial x} (2 x + y^{10})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 2 x + y ^{10}} \frac{\partial}{\partial x} (2 x + y^{10})

= \frac{1}{2 2 x + y ^{10}} \frac{\partial}{\partial x} (2 x + y^{10})

\frac{\partial}{\partial x} (2 x + y^{10}) = 2

= \frac{1}{2 2 x + y ^{10}} \cdot 2

Simplify

\frac{1}{2 2 x + y ^{10}} \cdot 2 : \frac{1}{2 x + y ^{10}}

= \frac{1}{2 x + y ^{10}}

\int (π^{2} - 1) d x

\int 4 x ln (6 x) d x

100 y^{^{''}} - 20 y^{^{'}} + y = 0

(x^{2} y + 3 y) y^{^{'}} = 2 x y^{2} + 8 x

\frac{d y}{d x} = e^{- 3 y}

What is (\partial)/(\partial x)(sqrt(2x+y^{10)}) ?
The answer to (\partial)/(\partial x)(sqrt(2x+y^{10)}) is 1/(sqrt(2x+y^{10))}