What is the derivative of f(x)=0.8e^xarctan(x) ?

The derivative of f(x)=0.8e^xarctan(x) is 0.8(e^xarctan(x)+(e^x)/(x^2+1))

What is the first derivative of f(x)=0.8e^xarctan(x) ?

The first derivative of f(x)=0.8e^xarctan(x) is 0.8(e^xarctan(x)+(e^x)/(x^2+1))

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derivative of

f (x) = 0.8 e^{x} arctan (x)

0.8 (e^{x} arctan (x) + \frac{e ^{x}}{x ^{2} + 1})

Solution steps

\frac{d}{d x} (0.8 e^{x} arctan (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.8 \frac{d}{d x} (e^{x} arctan (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = arctan (x)

= 0.8 (\frac{d}{d x} (e^{x}) arctan (x) + \frac{d}{d x} (arctan (x)) e^{x})

\frac{d}{d x} (e^{x}) = e^{x}

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

= 0.8 (e^{x} arctan (x) + \frac{1}{x ^{2} + 1} e^{x})

\frac{1}{x ^{2} + 1} e^{x} = \frac{e ^{x}}{x ^{2} + 1}

= 0.8 (e^{x} arctan (x) + \frac{e ^{x}}{x ^{2} + 1})

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What is the derivative of f(x)=0.8e^xarctan(x) ?
The derivative of f(x)=0.8e^xarctan(x) is 0.8(e^xarctan(x)+(e^x)/(x^2+1))
What is the first derivative of f(x)=0.8e^xarctan(x) ?
The first derivative of f(x)=0.8e^xarctan(x) is 0.8(e^xarctan(x)+(e^x)/(x^2+1))