What is the derivative of arcsin(cos(x^6)) ?

The derivative of arcsin(cos(x^6)) is -(6x^5sin(x^6))/(sqrt(sin^2(x^6)))

What is the first derivative of arcsin(cos(x^6)) ?

The first derivative of arcsin(cos(x^6)) is -(6x^5sin(x^6))/(sqrt(sin^2(x^6)))

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derivative of

arcsin (cos (x^{6}))

- \frac{6 x ^{5} sin ( x ^{6} )}{sin ^{2} ( x ^{6} )}

Solution steps

\frac{d}{d x} (arcsin (cos (x^{6})))

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{6})) = - sin (x^{6}) \cdot 6 x^{5}

= \frac{1}{1 - ( cos ( x ^{6} ) ) ^{2}} (- sin (x^{6}) \cdot 6 x^{5})

Simplify

\frac{1}{1 - cos ^{2} ( x ^{6} )} (- sin (x^{6}) \cdot 6 x^{5}) : - \frac{6 x ^{5} sin ( x ^{6} )}{sin ^{2} ( x ^{6} )}

= - \frac{6 x ^{5} sin ( x ^{6} )}{sin ^{2} ( x ^{6} )}

\frac{d}{d x} (lo g_{2 x + 1} (2 x + 3))

h \to 0 lim (\frac{6 x h + 3 h ^{2}}{h})

\frac{\partial}{\partial x} (3 e^{x^{3} y^{3}})

\int 7 x sin^{2} (x) d x

7 x + 4

What is the derivative of arcsin(cos(x^6)) ?
The derivative of arcsin(cos(x^6)) is -(6x^5sin(x^6))/(sqrt(sin^2(x^6)))
What is the first derivative of arcsin(cos(x^6)) ?
The first derivative of arcsin(cos(x^6)) is -(6x^5sin(x^6))/(sqrt(sin^2(x^6)))