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

The derivative of arctan((x+y^2)) is (2(x+y)(1+\frac{dy)/(dx))}{(x+y)^4+1}

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

The first derivative of arctan((x+y^2)) is (2(x+y)(1+\frac{dy)/(dx))}{(x+y)^4+1}

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

\frac{2 ( x + y ) ( 1 + \frac{d y}{d x} )}{( x + y ) ^{4} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( ( x + y ) ^{2} ) ^{2} + 1} \cdot 2 (x + y) (1 + \frac{d y}{d x}) : \frac{2 ( x + y ) ( 1 + \frac{d y}{d x} )}{( x + y ) ^{4} + 1}

= \frac{2 ( x + y ) ( 1 + \frac{d y}{d x} )}{( x + y ) ^{4} + 1}

x \to - 1 - lim (5 x + 2 p (x))

f (x) = \frac{5 ^{x}}{cos ( x )}

f (x) = (x - 3) (2 x + 1)

\frac{1}{2} \frac{d y}{d x} = y + 2

\frac{\partial}{\partial y} (sin (x) + cos (y))

What is the derivative of arctan((x+y^2)) ?
The derivative of arctan((x+y^2)) is (2(x+y)(1+\frac{dy)/(dx))}{(x+y)^4+1}
What is the first derivative of arctan((x+y^2)) ?
The first derivative of arctan((x+y^2)) is (2(x+y)(1+\frac{dy)/(dx))}{(x+y)^4+1}