What is the derivative of 37arctan(sqrt(x)) ?

The derivative of 37arctan(sqrt(x)) is (37)/(2sqrt(x)(x+1))

What is the first derivative of 37arctan(sqrt(x)) ?

The first derivative of 37arctan(sqrt(x)) is (37)/(2sqrt(x)(x+1))

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derivative of

37 arctan (x)

\frac{37}{2 x ( x + 1 )}

Solution steps

\frac{d}{d x} (37 arctan (x))

Take the constant out:

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

= 37 \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}

= 37 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x}

Simplify

37 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x} : \frac{37}{2 x ( x + 1 )}

= \frac{37}{2 x ( x + 1 )}

\frac{d y}{d x}, e^{4 x} = sin (x + 5 y)

\frac{e ^{x}}{1 + x}

y^{^{''}} - 4 y^{^{'}} + 6 y = e^{3 x} - 21

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

What is the derivative of 37arctan(sqrt(x)) ?
The derivative of 37arctan(sqrt(x)) is (37)/(2sqrt(x)(x+1))
What is the first derivative of 37arctan(sqrt(x)) ?
The first derivative of 37arctan(sqrt(x)) is (37)/(2sqrt(x)(x+1))