What is the derivative of arccos(ax) ?

The derivative of arccos(ax) is -a/(sqrt(1-a^2x^2))

What is the first derivative of arccos(ax) ?

The first derivative of arccos(ax) is -a/(sqrt(1-a^2x^2))

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derivative of

arccos (a x)

- \frac{a}{1 - a ^{2} x ^{2}}

Solution steps

\frac{d}{d x} (arccos (a x))

Apply the chain rule:

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

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

\frac{d}{d x} (a x) = a

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

Simplify

- \frac{1}{1 - ( a x ) ^{2}} a : - \frac{a}{1 - a ^{2} x ^{2}}

= - \frac{a}{1 - a ^{2} x ^{2}}

\frac{\partial}{\partial x} (x^{2} + y^{2} + 10)

\int_{0}^{\infty} 15 e^{- 5 x} d x

f (x) = 6 x - x^{2}, (1, 5)

f (x) = \frac{1}{x + 8}

y^{^{'}} - y = x e^{2 x} + 1

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