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derivative of arccos(x/b)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{b}) = \frac{1}{b}

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

Simplify

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

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

Popular Examples

(d^4)/(dx^4)((8x)/(1-x))

\frac{d ^{4}}{d x ^{4}} (\frac{8 x}{1 - x})

derivative of f(x)=5^{5x+1}+3^{1-3x}derivative of

f (x) = 5^{5 x + 1} + 3^{1 - 3 x}

y^{^{'}} + 5 y = 7

(d^2)/(dx^2)(-2x^4-2x^3+60x^2-22)

\frac{d ^{2}}{d x ^{2}} (- 2 x^{4} - 2 x^{3} + 60 x^{2} - 22)

derivative of 2xcos(x-2sin(x))

\frac{d}{d x} (2 x cos (x) - 2 sin (x))

Frequently Asked Questions (FAQ)

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