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

The derivative of arctan(x)-arctan(x-7) is (-14x+49)/((x^2+1)(x^2-14x+50))

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

The first derivative of arctan(x)-arctan(x-7) is (-14x+49)/((x^2+1)(x^2-14x+50))

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derivative of

arctan (x) - arctan (x - 7)

\frac{- 14 x + 49}{( x ^{2} + 1 ) ( x ^{2} - 14 x + 50 )}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (arctan (x - 7)) = \frac{1}{x ^{2} - 14 x + 50}

= \frac{1}{x ^{2} + 1} - \frac{1}{x ^{2} - 14 x + 50}

Simplify

\frac{1}{x ^{2} + 1} - \frac{1}{x ^{2} - 14 x + 50} : \frac{- 14 x + 49}{( x ^{2} + 1 ) ( x ^{2} - 14 x + 50 )}

= \frac{- 14 x + 49}{( x ^{2} + 1 ) ( x ^{2} - 14 x + 50 )}

3 e^{4 x} y^{^{'}} = - 16 \frac{x}{y ^{2}}, y (0) = 1

\frac{\partial}{\partial y} (\frac{y ^{4}}{x})

\frac{d}{d s} (s + t)

x \to \infty lim (538 \cdot x)

\int x^{4} ln (4 x) d x

What is the derivative of arctan(x)-arctan(x-7) ?
The derivative of arctan(x)-arctan(x-7) is (-14x+49)/((x^2+1)(x^2-14x+50))
What is the first derivative of arctan(x)-arctan(x-7) ?
The first derivative of arctan(x)-arctan(x-7) is (-14x+49)/((x^2+1)(x^2-14x+50))