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

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

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

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

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\frac{d}{d x} ((x + 2)^{a r c t a n (x)})

(\frac{ln ( x + 2 )}{x ^{2} + 1} + \frac{arctan ( x )}{x + 2}) (x + 2)^{a r c t a n (x)}

Solution steps

\frac{d}{d x} ((x + 2)^{a r c t a n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(x + 2)^{a r c t a n (x)} = e^{a r c t a n (x) l n (x + 2)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (x + 2)})

Apply the chain rule:

e^{a r c t a n (x) l n (x + 2)} \frac{d}{d x} (arctan (x) ln (x + 2))

= e^{a r c t a n (x) l n (x + 2)} \frac{d}{d x} (arctan (x) ln (x + 2))

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

= e^{a r c t a n (x) l n (x + 2)} (\frac{ln ( x + 2 )}{x ^{2} + 1} + \frac{arctan ( x )}{x + 2})

e^{a r c t a n (x) l n (x + 2)} = (x + 2)^{a r c t a n (x)}

= (\frac{ln ( x + 2 )}{x ^{2} + 1} + \frac{arctan ( x )}{x + 2}) (x + 2)^{a r c t a n (x)}

\frac{d}{d x} (1 - 2 x - x^{2})

\int_{0}^{1} 162 e^{2 x} + 324 d x

\int \frac{ln ^{3} ( x )}{x} d x

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

y = x - x^{2}, (- 1, - 2)

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