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Popular >

derivative of arcsin(sin(x-cos(x)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Popular Examples

tangent of (10x^3)/3+(13x^2)/2+4x+16 tangent of

\frac{10 x ^{3}}{3} + \frac{13 x ^{2}}{2} + 4 x + 16

integral of cos(t/2)

\int cos (\frac{t}{2}) d t

derivative of x^2-8x+13

\frac{d}{d x} (x^{2} - 8 x + 13)

derivative of (2x/(x^2))

\frac{d}{d x} (\frac{2 x}{x ^{2}})

y^3-(10x+4)+3xy^2y^'=0

y^{3} - (10 x + 4) + 3 x y^{2} y^{^{'}} = 0

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(sin(x-cos(x))) ?
The derivative of arcsin(sin(x-cos(x))) is 1/(sqrt(1-(sin(x)-cos(x))^2))(cos(x)+sin(x))
What is the first derivative of arcsin(sin(x-cos(x))) ?
The first derivative of arcsin(sin(x-cos(x))) is 1/(sqrt(1-(sin(x)-cos(x))^2))(cos(x)+sin(x))