What is implicit (dy)/(dx),y=(arctan(9x))^2 ?

The answer to implicit (dy)/(dx),y=(arctan(9x))^2 is (dy)/(dx)=(18arctan(9x))/(81x^2+1)

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implicit (dy)/(dx),y=(arctan(9x))^2

implicit derivative

\frac{d y}{d x}, y = (arctan (9 x))^{2}

\frac{d y}{d x} = \frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

Solution steps

y = (arctan (9 x))^{2}

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = \frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

\frac{d y}{d x} = \frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

\int_{0}^{\infty} \frac{1}{x ^{2} + 9} d x

x \to - 5 lim (\frac{1}{x ^{2} - 25})

\int \frac{x - 1}{x} d x

f (x) = ln (x^{3}), at x = e^{5}

f (x) = (x^{3} + 6 x)^{4}, at x = 2

What is implicit (dy)/(dx),y=(arctan(9x))^2 ?
The answer to implicit (dy)/(dx),y=(arctan(9x))^2 is (dy)/(dx)=(18arctan(9x))/(81x^2+1)