(d)/(dx)[arctan(-5x)]=? Choose 1 answer: (A) (-5)/(sqrt(1+25x^(2))) (B) (-5)/(sqrt(1-25x^(2))) (C) (-5)/(1+25x^(2)) (D) (-5)/(1-25x^(2))

Use Chain Rule: Use the chain rule for derivatives: (d/dx)[f(g(x))] = f'(g(x)) * g'(x).Identify Functions: Identify f(x) as arctan(x) and g(x) as -5x.Find f'(x): Find the derivative of f(x) = arctan(x), which is f'(x) = 1/(1+x^2).Find g'(x): Find the derivative of g(x) = -5x, which is g'(x) = -5.Apply Chain Rule: Apply the chain rule: (d/dx)[arctan(-5x)] = (1/(1+(-5x)^2)) * (-5).Simplify Expression: Simplify the expression: (1/(1+25x^2)) * (-5) = -5/(1+25x^2).

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(d)/(dx)[arctan(-5x)]=?
Choose 1 answer:
(A)
(-5)/(sqrt(1+25x^(2)))
(B)
(-5)/(sqrt(1-25x^(2)))
(C)
(-5)/(1+25x^(2))
(D)
(-5)/(1-25x^(2))

$\frac{d}{d x}[\arctan (-5 x)]=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{-5}{\sqrt{1+25 x^{2}}}$ $\newline$ (B) $\frac{-5}{\sqrt{1-25 x^{2}}}$ $\newline$ (C) $\frac{-5}{1+25 x^{2}}$ $\newline$ (D) $\frac{-5}{1-25 x^{2}}$

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Calculus

Find derivatives of using multiple formulae

Full solution

\frac{d}{d x}[\arctan (-5 x)]=?

\newline

Choose

1

answer:

\newline

(A)

\frac{-5}{\sqrt{1+25 x^{2}}}

\newline

(B)

\frac{-5}{\sqrt{1-25 x^{2}}}

\newline

(C)

\frac{-5}{1+25 x^{2}}

\newline

(D)

\frac{-5}{1-25 x^{2}}

Use Chain Rule: Use the chain rule for derivatives: $(\frac{d}{dx})[f(g(x))] = f'(g(x)) \cdot g'(x)$ .
Identify Functions: Identify $f(x)$ as $\arctan(x)$ and $g(x)$ as $-5x$ .
Find $f'(x)$ : Find the derivative of $f(x) = \arctan(x)$ , which is $f'(x) = \frac{1}{1+x^2}$ .
Find $g'(x)$ : Find the derivative of $g(x) = -5x$ , which is $g'(x) = -5$ .
Apply Chain Rule: Apply the chain rule: $(\frac{d}{dx})[\arctan(-5x)] = (\frac{1}{1+(-5x)^2}) \times (-5)$ .
Simplify Expression: Simplify the expression: $\frac{1}{1+25x^2}$ * $-5$ = $-\frac{5}{1+25x^2}$ .