What is the (xsqrt(4-x^2))^' ?

The (xsqrt(4-x^2))^' is (-2x^2+4)/(sqrt(4-x^2))

What is the first (xsqrt(4-x^2))^' ?

The first (xsqrt(4-x^2))^' is (-2x^2+4)/(sqrt(4-x^2))

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(x 4 - x^{2})^{^{'}}

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

Solution steps

(x 4 - x^{2})^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 4 - x^{2}

= x^{^{'}} 4 - x^{2} + (4 - x^{2})^{^{'}} x

x^{'} = 1

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

= 1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x

Simplify

1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x : \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

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

n = 1 \sum \infty \frac{1 ^{n}}{n ^{7}}

x \to 0 lim (\frac{x ^{2}}{∣ x ∣})

y^{^{'}} = t^{2} y^{2}

f (x) = 2 x^{3} - 6 x^{2}

\int \frac{sin ^{4} ( x )}{4} d x

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