What is the derivative of arctan(3x^2) ?

The derivative of arctan(3x^2) is (6x)/(9x^4+1)

What is the first derivative of arctan(3x^2) ?

The first derivative of arctan(3x^2) is (6x)/(9x^4+1)

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\frac{d}{d x} (arctan (3 x^{2}))

\frac{6 x}{9 x ^{4} + 1}

Solution steps

\frac{d}{d x} (arctan (3 x^{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

= \frac{1}{( 3 x ^{2} ) ^{2} + 1} \cdot 6 x

Simplify

\frac{1}{( 3 x ^{2} ) ^{2} + 1} \cdot 6 x : \frac{6 x}{9 x ^{4} + 1}

= \frac{6 x}{9 x ^{4} + 1}

\int_{0}^{\infty} x e^{- b x} d x

y = \frac{x}{x + 6}, (4, 0.2)

\int x^{2} (x^{3} - 11)^{6} d x

n = 1 \sum \infty \frac{1}{1 + 2 ^{n}}

ln (1 + x^{5})

What is the derivative of arctan(3x^2) ?
The derivative of arctan(3x^2) is (6x)/(9x^4+1)
What is the first derivative of arctan(3x^2) ?
The first derivative of arctan(3x^2) is (6x)/(9x^4+1)