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

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

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

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

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derivative of

e^{a r c t a n (3 x^{2})}

\frac{6 e ^{a r c t a n (3 x^{2})} x}{9 x ^{4} + 1}

Solution steps

\frac{d}{d x} (e^{a r c t a n (3 x^{2})})

Apply the chain rule:

e^{a r c t a n (3 x^{2})} \frac{d}{d x} (arctan (3 x^{2}))

= e^{a r c t a n (3 x^{2})} \frac{d}{d x} (arctan (3 x^{2}))

\frac{d}{d x} (arctan (3 x^{2})) = \frac{6 x}{9 x ^{4} + 1}

= e^{a r c t a n (3 x^{2})} \frac{6 x}{9 x ^{4} + 1}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 e ^{a r c t a n (3 x^{2})} x}{9 x ^{4} + 1}

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

\frac{\partial ^{2}}{\partial y ^{2}} (y^{5} sin (3 x))

\frac{e ^{x} + e ^{- x}}{2}

\int 2 x (x^{2} + 7)^{9} d x

n = 1 \sum \infty \frac{1}{5 n ^{2} - n}

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