What is the derivative of x^2arctan(7x) ?

The derivative of x^2arctan(7x) is 2xarctan(7x)+(7x^2)/(49x^2+1)

What is the first derivative of x^2arctan(7x) ?

The first derivative of x^2arctan(7x) is 2xarctan(7x)+(7x^2)/(49x^2+1)

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\frac{d}{d x} (x^{2} arctan (7 x))

2 x arctan (7 x) + \frac{7 x ^{2}}{49 x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} arctan (7 x))

Apply the Product Rule:

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

f = x^{2}, g = arctan (7 x)

= \frac{d}{d x} (x^{2}) arctan (7 x) + \frac{d}{d x} (arctan (7 x)) x^{2}

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

\frac{d}{d x} (arctan (7 x)) = \frac{7}{49 x ^{2} + 1}

= 2 x arctan (7 x) + \frac{7}{49 x ^{2} + 1} x^{2}

Multiply fractions:

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

= 2 x arctan (7 x) + \frac{7 x ^{2}}{49 x ^{2} + 1}

\int \frac{6 x - 1}{x ^{3} + 4 x} d x

\int 5 x^{3} e^{x} d x

y = ln (x + 1)

\frac{d}{d x} (2 e^{- 2 x})

\frac{d}{d x} (cos^{- 2} (x))

What is the derivative of x^2arctan(7x) ?
The derivative of x^2arctan(7x) is 2xarctan(7x)+(7x^2)/(49x^2+1)
What is the first derivative of x^2arctan(7x) ?
The first derivative of x^2arctan(7x) is 2xarctan(7x)+(7x^2)/(49x^2+1)