What is the derivative of xsqrt(4-x^2)+4arcsin(x/2) ?

The derivative of xsqrt(4-x^2)+4arcsin(x/2) is 2sqrt(-x^2+4)

What is the first derivative of xsqrt(4-x^2)+4arcsin(x/2) ?

The first derivative of xsqrt(4-x^2)+4arcsin(x/2) is 2sqrt(-x^2+4)

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\frac{d}{d x} (x 4 - x^{2} + 4 arcsin (\frac{x}{2}))

2 - x^{2} + 4

Solution steps

\frac{d}{d x} (x 4 - x^{2} + 4 arcsin (\frac{x}{2}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x 4 - x^{2}) + \frac{d}{d x} (4 arcsin (\frac{x}{2}))

\frac{d}{d x} (x 4 - x^{2}) = \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

\frac{d}{d x} (4 arcsin (\frac{x}{2})) = \frac{4}{4 - x ^{2}}

= \frac{- 2 x ^{2} + 4}{4 - x ^{2}} + \frac{4}{4 - x ^{2}}

Simplify

\frac{- 2 x ^{2} + 4}{4 - x ^{2}} + \frac{4}{4 - x ^{2}} : 2 - x^{2} + 4

= 2 - x^{2} + 4

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

f (x) = 8 e^{x}

x y^{^{'}} + y = e^{x}, y (1) = 7

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

x^{4} + 9 x

What is the derivative of xsqrt(4-x^2)+4arcsin(x/2) ?
The derivative of xsqrt(4-x^2)+4arcsin(x/2) is 2sqrt(-x^2+4)
What is the first derivative of xsqrt(4-x^2)+4arcsin(x/2) ?
The first derivative of xsqrt(4-x^2)+4arcsin(x/2) is 2sqrt(-x^2+4)