What is the derivative of arctan({g}(x)(x)) ?

The derivative of arctan({g}(x)(x)) is (x derivative of {g}(x))/({g)(x)^2+1}+arctan({g}(x))

What is the first derivative of arctan({g}(x)(x)) ?

The first derivative of arctan({g}(x)(x)) is (x derivative of {g}(x))/({g)(x)^2+1}+arctan({g}(x))

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\frac{d}{d x} (arctan (g (x)) (x))

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

Solution steps

\frac{d}{d x} (arctan (g (x)) (x))

Apply the Product Rule:

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

f = arctan (g (x)), g = x

= \frac{d}{d x} (arctan (g (x))) x + \frac{d x}{d x} arctan (g (x))

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\frac{\partial}{\partial x} (3 sin (\frac{6 x}{y}))

x \to - \infty lim (\frac{5 + 2 x}{9 + 4 x ^{2}})

\int \frac{x + 3}{4 - x ^{2}} d x

2 x + 1, at x = \frac{1}{4}

n = 1 \sum \infty e^{- n} n!

What is the derivative of arctan({g}(x)(x)) ?
The derivative of arctan({g}(x)(x)) is (x derivative of {g}(x))/({g)(x)^2+1}+arctan({g}(x))
What is the first derivative of arctan({g}(x)(x)) ?
The first derivative of arctan({g}(x)(x)) is (x derivative of {g}(x))/({g)(x)^2+1}+arctan({g}(x))