What is the derivative of f(x)=x^2arctan(x3^x) ?

The derivative of f(x)=x^2arctan(x3^x) is 2xarctan(3^xx)+(x^2(3^x+ln(3)*3^xx))/(9^xx^2+1)

What is the first derivative of f(x)=x^2arctan(x3^x) ?

The first derivative of f(x)=x^2arctan(x3^x) is 2xarctan(3^xx)+(x^2(3^x+ln(3)*3^xx))/(9^xx^2+1)

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derivative of

f (x) = x^{2} arctan (x 3^{x})

2 x arctan (3^{x} x) + \frac{x ^{2} ( 3 ^{x} + ln ( 3 ) \cdot 3 ^{x} x )}{9 ^{x} x ^{2} + 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = arctan (x 3^{x})

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

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

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

= 2 x arctan (x \cdot 3^{x}) + \frac{3 ^{x} + ln ( 3 ) \cdot 3 ^{x} x}{9 ^{x} x ^{2} + 1} x^{2}

Multiply fractions:

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

= 2 x arctan (3^{x} x) + \frac{x ^{2} ( 3 ^{x} + ln ( 3 ) \cdot 3 ^{x} x )}{9 ^{x} x ^{2} + 1}

\int_{0}^{1} 2 π x (4 e^{- x^{2}}) d x

y = ln (3^{3 x})

{\frac{s}{( s + 2 ) ( s ^{2} + 4 )}}

\frac{d}{d x} (2 e^{3 x^{2} + 6 x + 7})

\int cos (3 x - 2) d x

What is the derivative of f(x)=x^2arctan(x3^x) ?
The derivative of f(x)=x^2arctan(x3^x) is 2xarctan(3^xx)+(x^2(3^x+ln(3)*3^xx))/(9^xx^2+1)
What is the first derivative of f(x)=x^2arctan(x3^x) ?
The first derivative of f(x)=x^2arctan(x3^x) is 2xarctan(3^xx)+(x^2(3^x+ln(3)*3^xx))/(9^xx^2+1)