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Popular >

derivative of arcsin(sin(x))

Solution

derivative of

arcsin (sin (x))

Solution

sec (x) cos^{2} (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= sec (x) cos^{2} (x)

Popular Examples

derivative of 1/(xln(10))

\frac{d}{d x} (\frac{1}{x ln ( 10 )})

derivative of f(x)=(1+e^x)/(1-e^x)derivative of

f (x) = \frac{1 + e ^{x}}{1 - e ^{x}}

(dy)/(dx)=e^{(3x+2y)}

\frac{d y}{d x} = e^{(3 x + 2 y)}

tangent of f(x)=sqrt(x^2+3x),\at x=1 tangent of

f (x) = x^{2} + 3 x, at x = 1

derivative of 4-(15/(4x^{1/4)})

\frac{d}{d x} (4 - \frac{15}{4 x ^{\frac{1}{4}}})

Frequently Asked Questions (FAQ)

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