What is (\partial)/(\partial x)(arctan(2x+y)) ?

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

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(\partial)/(\partial x)(arctan(2x+y))

\frac{\partial}{\partial x} (arctan (2 x + y))

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

Solution steps

\frac{\partial}{\partial x} (arctan (2 x + y))

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

y (1 + x^{2}) y^{^{'}} - x (4 + y^{2}) = 0

\int 9 sin^{3} (x) cos^{2} (x) d x

y^{^{'}} = \frac{2 x y ^{3}}{1 - x ^{2} y ^{2}}

f^{^{'}} (x) = - 3

x \to 0 lim (7 - x^{2})

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