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Popular >

derivative of 39arctan(sqrt(x))

Solution

\frac{d}{d x} (39 arctan (x))

Solution

\frac{39}{2 x ( x + 1 )}

Solution steps

\frac{d}{d x} (39 arctan (x))

Take the constant out:

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

= 39 \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}

= 39 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x}

Simplify

39 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x} : \frac{39}{2 x ( x + 1 )}

= \frac{39}{2 x ( x + 1 )}

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Frequently Asked Questions (FAQ)

What is the derivative of 39arctan(sqrt(x)) ?
The derivative of 39arctan(sqrt(x)) is (39)/(2sqrt(x)(x+1))
What is the first derivative of 39arctan(sqrt(x)) ?
The first derivative of 39arctan(sqrt(x)) is (39)/(2sqrt(x)(x+1))