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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

x \to \infty lim (ln (- 1))

\frac{sin ( x ^{3} )}{x}

\frac{d}{d x} (x - y)

3 cos (3 t)

y^{^{''}} + 8 y^{^{'}} + 19 y = 0, y (0) = 3, y^{^{'}} (0) = - 4

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