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Popular Calculus >

derivative of (1+x^2arctan(x))

Solution

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

Solution

2 x arctan (x) + 1

Solution steps

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

Apply the Product Rule:

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

f = 1 + x^{2}, g = arctan (x)

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

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

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

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

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

= 2 x arctan (x) + 1

Graph

Popular Examples

derivative of x^3y-y^2

d er i v a t i v e x^{3} y - y^{2}

integral of (tan(4x)+sec(4x))^2

\int (tan (4 x) + sec (4 x))^{2} d x

(\partial)/(\partial x)(e^{3x-y})

\frac{\partial}{\partial x} (e^{3 x - y})

tangent of f(x)=3e^{1-x^2},(1,3)

t an g e n t f (x) = 3 e^{1 - x^{2}}, (1, 3)

sum from n=0 to infinity of-1/(5^n)

n = 0 \sum \infty - \frac{1}{5 ^{n}}

Frequently Asked Questions (FAQ)

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