What is (\partial)/(\partial y)(arctan(x+6y)) ?

The answer to (\partial)/(\partial y)(arctan(x+6y)) is 6/((x+6y)^2+1)

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(\partial)/(\partial y)(arctan(x+6y))

\frac{\partial}{\partial y} (arctan (x + 6 y))

\frac{6}{( x + 6 y ) ^{2} + 1}

Solution steps

\frac{\partial}{\partial y} (arctan (x + 6 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{( x + 6 y ) ^{2} + 1} \frac{\partial}{\partial y} (x + 6 y)

= \frac{1}{( x + 6 y ) ^{2} + 1} \frac{\partial}{\partial y} (x + 6 y)

\frac{\partial}{\partial y} (x + 6 y) = 6

= \frac{1}{( x + 6 y ) ^{2} + 1} \cdot 6

Simplify

\frac{1}{( x + 6 y ) ^{2} + 1} \cdot 6 : \frac{6}{( x + 6 y ) ^{2} + 1}

= \frac{6}{( x + 6 y ) ^{2} + 1}

y = x^{2} + 3

\int_{1}^{4} \frac{7}{x ^{2}} d x

(9 x + 3) + (9 y - 9) y^{^{'}} = 0

\int_{0}^{3} (x + 9 - x^{2}) d x

\int_{1}^{2} cos (x^{2}) d x

What is (\partial)/(\partial y)(arctan(x+6y)) ?
The answer to (\partial)/(\partial y)(arctan(x+6y)) is 6/((x+6y)^2+1)