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Popular Calculus >

derivative of 4arccos(-5x)

Solution

\frac{d}{d x} (4 arccos (- 5 x))

Solution

\frac{20}{1 - 25 x ^{2}}

Solution steps

\frac{d}{d x} (4 arccos (- 5 x))

Take the constant out:

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

= 4 \frac{d}{d x} (arccos (- 5 x))

Apply the chain rule:

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

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

\frac{d}{d x} (- 5 x) = - 5

= 4 - \frac{1}{1 - ( - 5 x ) ^{2}} (- 5)

Simplify

4 - \frac{1}{1 - ( - 5 x ) ^{2}} (- 5) : \frac{20}{1 - 25 x ^{2}}

= \frac{20}{1 - 25 x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 4arccos(-5x) ?
The derivative of 4arccos(-5x) is (20)/(sqrt(1-25x^2))
What is the first derivative of 4arccos(-5x) ?
The first derivative of 4arccos(-5x) is (20)/(sqrt(1-25x^2))