What is the derivative of f(x)=arctan(3x) ?

The derivative of f(x)=arctan(3x) is 3/(9x^2+1)

What is the first derivative of f(x)=arctan(3x) ?

The first derivative of f(x)=arctan(3x) is 3/(9x^2+1)

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derivative of

f (x) = arctan (3 x)

\frac{3}{9 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (3 x))

Apply the chain rule:

\frac{1}{( 3 x ) ^{2} + 1} \frac{d}{d x} (3 x)

= \frac{1}{( 3 x ) ^{2} + 1} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= \frac{1}{( 3 x ) ^{2} + 1} \cdot 3

Simplify

\frac{1}{( 3 x ) ^{2} + 1} \cdot 3 : \frac{3}{9 x ^{2} + 1}

= \frac{3}{9 x ^{2} + 1}

\frac{s + 1}{s ^{2} + 4}

\frac{( x ^{2} + 2 ) ^{\frac{3}{2}}}{3}

f^{^{'}} (x) = tan (x) + cot (x)

\int sin (a t) d t

\frac{d y}{d x} + y cos (x) = 5 cos (x)

What is the derivative of f(x)=arctan(3x) ?
The derivative of f(x)=arctan(3x) is 3/(9x^2+1)
What is the first derivative of f(x)=arctan(3x) ?
The first derivative of f(x)=arctan(3x) is 3/(9x^2+1)