What is (\partial)/(\partial x)(arctan(9x)) ?

The answer to (\partial)/(\partial x)(arctan(9x)) is 9/(81x^2+1)

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(\partial)/(\partial x)(arctan(9x))

\frac{\partial}{\partial x} (arctan (9 x))

\frac{9}{81 x ^{2} + 1}

Solution steps

\frac{\partial}{\partial x} (arctan (9 x))

Apply the chain rule:

\frac{1}{( 9 x ) ^{2} + 1} \frac{\partial}{\partial x} (9 x)

= \frac{1}{( 9 x ) ^{2} + 1} \frac{\partial}{\partial x} (9 x)

\frac{\partial}{\partial x} (9 x) = 9

= \frac{1}{( 9 x ) ^{2} + 1} \cdot 9

Simplify

\frac{1}{( 9 x ) ^{2} + 1} \cdot 9 : \frac{9}{81 x ^{2} + 1}

= \frac{9}{81 x ^{2} + 1}

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

\int 18 arctan (x) d x

\frac{d ^{2}}{d x ^{2}} (\frac{2 x - 3}{3 x + 1})

f (x) = x^{4} + 2 \cdot e^{x}, at x = 0

\int 5 sin (\frac{nπ x}{4}) d x

What is (\partial)/(\partial x)(arctan(9x)) ?
The answer to (\partial)/(\partial x)(arctan(9x)) is 9/(81x^2+1)