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

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

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(\partial)/(\partial y)(arctan(x+4y))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 4 lim (3 x^{2})

f (x) = x + 6, at x = 10

10 \cdot \frac{1 - 3 s}{1 + 6 s}

y = 4 x^{3} - 2 x, (- 1, - 2)

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

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