What is the derivative of cos(arcsin(x+3)) ?

The derivative of cos(arcsin(x+3)) is -(x+3)/(sqrt(-x^2-6x-8))

What is the first derivative of cos(arcsin(x+3)) ?

The first derivative of cos(arcsin(x+3)) is -(x+3)/(sqrt(-x^2-6x-8))

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derivative of

cos (arcsin (x + 3))

- \frac{x + 3}{- x ^{2} - 6 x - 8}

Solution steps

\frac{d}{d x} (cos (arcsin (x + 3)))

Simplify

cos (arcsin (x + 3)) : - x^{2} - 6 x - 8

= \frac{d}{d x} (- x^{2} - 6 x - 8)

Apply the chain rule:

\frac{1}{2 - x ^{2} - 6 x - 8} \frac{d}{d x} (- x^{2} - 6 x - 8)

= \frac{1}{2 - x ^{2} - 6 x - 8} \frac{d}{d x} (- x^{2} - 6 x - 8)

\frac{d}{d x} (- x^{2} - 6 x - 8) = - 2 x - 6

= \frac{1}{2 - x ^{2} - 6 x - 8} (- 2 x - 6)

Simplify

\frac{1}{2 - x ^{2} - 6 x - 8} (- 2 x - 6) : - \frac{x + 3}{- x ^{2} - 6 x - 8}

= - \frac{x + 3}{- x ^{2} - 6 x - 8}

\frac{2}{s ( s ^{2} + 4 s + 5 )}

\int x (x - 4) d x

\int \frac{1}{e ^{2 x - 1}} d x

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

\int \frac{7 x ^{3} - 7 x + 5}{x ^{3} - x ^{2}} d x

What is the derivative of cos(arcsin(x+3)) ?
The derivative of cos(arcsin(x+3)) is -(x+3)/(sqrt(-x^2-6x-8))
What is the first derivative of cos(arcsin(x+3)) ?
The first derivative of cos(arcsin(x+3)) is -(x+3)/(sqrt(-x^2-6x-8))