What is the derivative of arctan(7x) ?

The derivative of arctan(7x) is 7/(49x^2+1)

What is the first derivative of arctan(7x) ?

The first derivative of arctan(7x) is 7/(49x^2+1)

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\frac{d}{d x} (arctan (7 x))

\frac{7}{49 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (7 x))

Apply the chain rule:

\frac{1}{( 7 x ) ^{2} + 1} \frac{d}{d x} (7 x)

= \frac{1}{( 7 x ) ^{2} + 1} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= \frac{1}{( 7 x ) ^{2} + 1} \cdot 7

Simplify

\frac{1}{( 7 x ) ^{2} + 1} \cdot 7 : \frac{7}{49 x ^{2} + 1}

= \frac{7}{49 x ^{2} + 1}

y^{^{'}} = x - y + 1

f (x) = \frac{1300 + 8 x - 0.0004 x ^{2}}{x}

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

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

f^{^{''}} (x) = 2 x

What is the derivative of arctan(7x) ?
The derivative of arctan(7x) is 7/(49x^2+1)
What is the first derivative of arctan(7x) ?
The first derivative of arctan(7x) is 7/(49x^2+1)