What is the derivative of 11arctan(sqrt(x)) ?

The derivative of 11arctan(sqrt(x)) is (11)/(2sqrt(x)(x+1))

What is the first derivative of 11arctan(sqrt(x)) ?

The first derivative of 11arctan(sqrt(x)) is (11)/(2sqrt(x)(x+1))

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\frac{d}{d x} (11 arctan (x))

\frac{11}{2 x ( x + 1 )}

Solution steps

\frac{d}{d x} (11 arctan (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 11 \frac{d}{d x} (arctan (x))

Apply the chain rule:

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

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

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

= 11 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x}

Simplify

11 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x} : \frac{11}{2 x ( x + 1 )}

= \frac{11}{2 x ( x + 1 )}

x \to 5 + lim (\frac{( x + 1 )}{x - 5})

3 x^{2} - 2 x

\int \frac{s}{s ^{2} + 3 s + 6} d s

x = - 2 y^{2} + 3 y - 5, x + 3 y = - 13

f (x) = 2 x + 1

What is the derivative of 11arctan(sqrt(x)) ?
The derivative of 11arctan(sqrt(x)) is (11)/(2sqrt(x)(x+1))
What is the first derivative of 11arctan(sqrt(x)) ?
The first derivative of 11arctan(sqrt(x)) is (11)/(2sqrt(x)(x+1))