What is the derivative of f(x)=7arctan(7x) ?

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

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

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

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derivative of

f (x) = 7 arctan (7 x)

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

Solution steps

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

Take the constant out:

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

= 7 \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

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

Simplify

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

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

y = - 8 x ln (6 x + 5)

\int_{0}^{1} (x + 3) (x - 4) d x

y = (x^{3} - 16 x)^{12}, (4, 0)

\frac{d}{d y} (arctan (x + 2 y))

x \to 2 lim (20 - x^{2})

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