What is the derivative of arctan(10x) ?

The derivative of arctan(10x) is (10)/(100x^2+1)

What is the first derivative of arctan(10x) ?

The first derivative of arctan(10x) is (10)/(100x^2+1)

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\frac{d}{d x} (arctan (10 x))

\frac{10}{100 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (10 x))

Apply the chain rule:

\frac{1}{( 10 x ) ^{2} + 1} \frac{d}{d x} (10 x)

= \frac{1}{( 10 x ) ^{2} + 1} \frac{d}{d x} (10 x)

\frac{d}{d x} (10 x) = 10

= \frac{1}{( 10 x ) ^{2} + 1} \cdot 10

Simplify

\frac{1}{( 10 x ) ^{2} + 1} \cdot 10 : \frac{10}{100 x ^{2} + 1}

= \frac{10}{100 x ^{2} + 1}

\frac{d}{d x} (ln (x^{2} - 9))

x^{2} + (\frac{1}{2} x - 5)^{2}

f (x) = 6 x sin (x)

\frac{d y}{d x} = x x - 9

What is the derivative of arctan(10x) ?
The derivative of arctan(10x) is (10)/(100x^2+1)
What is the first derivative of arctan(10x) ?
The first derivative of arctan(10x) is (10)/(100x^2+1)