What is the derivative of sin(x+arcsin(x)) ?

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

What is the first derivative of sin(x+arcsin(x)) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

12 x^{3} - 3 y^{2} x^{4} + 1 (\frac{d y}{d x}) = 0

\int_{0}^{\frac{1}{2}} (2 x - 1)^{- 3} d x

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

\frac{\partial}{\partial x} (\frac{1}{x ^{2} - y ^{2}})

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