What is the derivative of (e^{arctan(x})/(1+x^2)) ?

The derivative of (e^{arctan(x})/(1+x^2)) is (e^{arctan(x)}-2e^{arctan(x)}x)/((1+x^2)^2)

What is the first derivative of (e^{arctan(x})/(1+x^2)) ?

The first derivative of (e^{arctan(x})/(1+x^2)) is (e^{arctan(x)}-2e^{arctan(x)}x)/((1+x^2)^2)

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\frac{d}{d x} (\frac{e ^{a r c t a n (x)}}{1 + x ^{2}})

\frac{e ^{a r c t a n (x)} - 2 e ^{a r c t a n (x)} x}{( 1 + x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{a r c t a n (x)}}{1 + x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{a r c t a n (x)} ) ( 1 + x ^{2} ) - \frac{d}{d x} ( 1 + x ^{2} ) e ^{a r c t a n (x)}}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (e^{a r c t a n (x)}) = \frac{e ^{a r c t a n (x)}}{x ^{2} + 1}

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

= \frac{\frac{e ^{a r c t a n (x)}}{x ^{2} + 1} ( 1 + x ^{2} ) - 2 x e ^{a r c t a n (x)}}{( 1 + x ^{2} ) ^{2}}

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

= \frac{e ^{a r c t a n (x)} - 2 e ^{a r c t a n (x)} x}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (\frac{csc ( 3 x )}{x ^{3}})

\int \frac{x - 4}{x ^{9}} d x

\frac{d}{d x} (x^{\frac{5}{3}})

2 t e^{- 5 t}

\frac{d}{d x} (10 x - 1.86 x^{2})

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