What is the derivative of cos(arcsin(x+5)) ?

The derivative of cos(arcsin(x+5)) is -(x+5)/(sqrt(-x^2-10x-24))

What is the first derivative of cos(arcsin(x+5)) ?

The first derivative of cos(arcsin(x+5)) is -(x+5)/(sqrt(-x^2-10x-24))

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derivative of

cos (arcsin (x + 5))

- \frac{x + 5}{- x ^{2} - 10 x - 24}

Solution steps

\frac{d}{d x} (cos (arcsin (x + 5)))

Simplify

cos (arcsin (x + 5)) : - x^{2} - 10 x - 24

= \frac{d}{d x} (- x^{2} - 10 x - 24)

Apply the chain rule:

\frac{1}{2 - x ^{2} - 10 x - 24} \frac{d}{d x} (- x^{2} - 10 x - 24)

= \frac{1}{2 - x ^{2} - 10 x - 24} \frac{d}{d x} (- x^{2} - 10 x - 24)

\frac{d}{d x} (- x^{2} - 10 x - 24) = - 2 x - 10

= \frac{1}{2 - x ^{2} - 10 x - 24} (- 2 x - 10)

Simplify

\frac{1}{2 - x ^{2} - 10 x - 24} (- 2 x - 10) : - \frac{x + 5}{- x ^{2} - 10 x - 24}

= - \frac{x + 5}{- x ^{2} - 10 x - 24}

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What is the derivative of cos(arcsin(x+5)) ?
The derivative of cos(arcsin(x+5)) is -(x+5)/(sqrt(-x^2-10x-24))
What is the first derivative of cos(arcsin(x+5)) ?
The first derivative of cos(arcsin(x+5)) is -(x+5)/(sqrt(-x^2-10x-24))