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

The derivative of arcsin(cos(x^3)) is -(3x^2sin(x^3))/(sqrt(sin^2(x^3)))

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

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

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derivative of

arcsin (cos (x^{3}))

- \frac{3 x ^{2} sin ( x ^{3} )}{sin ^{2} ( x ^{3} )}

Solution steps

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

Apply the chain rule:

\frac{1}{1 - ( cos ( x ^{3} ) ) ^{2}} \frac{d}{d x} (cos (x^{3}))

= \frac{1}{1 - ( cos ( x ^{3} ) ) ^{2}} \frac{d}{d x} (cos (x^{3}))

\frac{d}{d x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

= \frac{1}{1 - ( cos ( x ^{3} ) ) ^{2}} (- sin (x^{3}) \cdot 3 x^{2})

Simplify

\frac{1}{1 - cos ^{2} ( x ^{3} )} (- sin (x^{3}) \cdot 3 x^{2}) : - \frac{3 x ^{2} sin ( x ^{3} )}{sin ^{2} ( x ^{3} )}

= - \frac{3 x ^{2} sin ( x ^{3} )}{sin ^{2} ( x ^{3} )}

f (x) = 3 x - 2 x, at x = 1

\frac{\partial}{\partial y} (\frac{9 y}{x ^{5}})

y^{^{''}} + 22 y = 0

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

10 - 7 x, y = 0, x^{2} - 20

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