What is the derivative of arcsin(cos(x^8)) ?

The derivative of arcsin(cos(x^8)) is -(8x^7sin(x^8))/(sqrt(sin^2(x^8)))

What is the first derivative of arcsin(cos(x^8)) ?

The first derivative of arcsin(cos(x^8)) is -(8x^7sin(x^8))/(sqrt(sin^2(x^8)))

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derivative of

arcsin (cos (x^{8}))

- \frac{8 x ^{7} sin ( x ^{8} )}{sin ^{2} ( x ^{8} )}

Solution steps

\frac{d}{d x} (arcsin (cos (x^{8})))

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{8})) = - sin (x^{8}) \cdot 8 x^{7}

= \frac{1}{1 - ( cos ( x ^{8} ) ) ^{2}} (- sin (x^{8}) \cdot 8 x^{7})

Simplify

\frac{1}{1 - cos ^{2} ( x ^{8} )} (- sin (x^{8}) \cdot 8 x^{7}) : - \frac{8 x ^{7} sin ( x ^{8} )}{sin ^{2} ( x ^{8} )}

= - \frac{8 x ^{7} sin ( x ^{8} )}{sin ^{2} ( x ^{8} )}

\frac{d}{d x} (sin (m arcsin (x)))

n = 1 \sum \infty \frac{3}{4 + 8 ^{n}}

\int 1 - 2 x d x

\int sin (x) + sinh (x) d x

\frac{d y}{d x} = \frac{( 10 + 15 x )}{x y ^{2}}, y (1) = 3

What is the derivative of arcsin(cos(x^8)) ?
The derivative of arcsin(cos(x^8)) is -(8x^7sin(x^8))/(sqrt(sin^2(x^8)))
What is the first derivative of arcsin(cos(x^8)) ?
The first derivative of arcsin(cos(x^8)) is -(8x^7sin(x^8))/(sqrt(sin^2(x^8)))