What is the derivative of arccos(5x) ?

The derivative of arccos(5x) is -5/(sqrt(1-25x^2))

What is the first derivative of arccos(5x) ?

The first derivative of arccos(5x) is -5/(sqrt(1-25x^2))

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derivative of

arccos (5 x)

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

Solution steps

\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

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

Simplify

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

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

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