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Popular >

derivative of arcsin(cos(x))

Solution

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

Solution

- csc (x) sin^{2} (x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

= - csc (x) sin^{2} (x)

Popular Examples

inverse oflaplace (s+1)/(s(s-1)^2)inverse laplace

\frac{s + 1}{s ( s - 1 ) ^{2}}

(\partial)/(\partial x)(e^{-(x+y)})

\frac{\partial}{\partial x} (e^{- (x + y)})

(t^2-1)y^'+2ty^2=0

(t^{2} - 1) y^{^{'}} + 2 t y^{2} = 0

integral of (t^2)/((a+bt^3)^2)

\int \frac{t ^{2}}{( a + b t ^{3} ) ^{2}} d t

xy^'=2x^2y+3x^3e^{x^2}

x y^{^{'}} = 2 x^{2} y + 3 x^{3} e^{x^{2}}

Frequently Asked Questions (FAQ)

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