What is the (xsqrt(1-x^2))^' ?

The (xsqrt(1-x^2))^' is (-2x^2+1)/(sqrt(1-x^2))

What is the first (xsqrt(1-x^2))^' ?

The first (xsqrt(1-x^2))^' is (-2x^2+1)/(sqrt(1-x^2))

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(x 1 - x^{2})^{^{'}}

\frac{- 2 x ^{2} + 1}{1 - x ^{2}}

Solution steps

(x 1 - x^{2})^{'}

Apply the Product Rule:

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

f = x, g = 1 - x^{2}

= x^{^{'}} 1 - x^{2} + (1 - x^{2})^{^{'}} x

x^{'} = 1

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

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

Simplify

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

= \frac{- 2 x ^{2} + 1}{1 - x ^{2}}

\int \frac{sec ^{2} ( y )}{tan ( y )} d y

\frac{d}{d x} (sin^{2} (tan (4 x)))

\int tan (θ) sec (θ) d θ

y^{^{'}} = e^{4 x + y}

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

What is the (xsqrt(1-x^2))^' ?
The (xsqrt(1-x^2))^' is (-2x^2+1)/(sqrt(1-x^2))
What is the first (xsqrt(1-x^2))^' ?
The first (xsqrt(1-x^2))^' is (-2x^2+1)/(sqrt(1-x^2))