What is the derivative of xsqrt(8-x^2) ?

The derivative of xsqrt(8-x^2) is (-2x^2+8)/(sqrt(8-x^2))

What is the first derivative of xsqrt(8-x^2) ?

The first derivative of xsqrt(8-x^2) is (-2x^2+8)/(sqrt(8-x^2))

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derivative of

x 8 - x^{2}

\frac{- 2 x ^{2} + 8}{8 - x ^{2}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 8 - x^{2}

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

\frac{d x}{d x} = 1

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

= 1 \cdot 8 - x^{2} + (- \frac{x}{8 - x ^{2}}) x

Simplify

1 \cdot 8 - x^{2} + (- \frac{x}{8 - x ^{2}}) x : \frac{- 2 x ^{2} + 8}{8 - x ^{2}}

= \frac{- 2 x ^{2} + 8}{8 - x ^{2}}

\int \frac{1}{( 4 + x ^{2} ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (x^{4} + x y^{3})

x \to 0 + lim (\frac{e ^{x}}{x})

x \to 5 lim (8 x + 9)

\int \frac{( x + 6 ) ^{5}}{2 x} d x

What is the derivative of xsqrt(8-x^2) ?
The derivative of xsqrt(8-x^2) is (-2x^2+8)/(sqrt(8-x^2))
What is the first derivative of xsqrt(8-x^2) ?
The first derivative of xsqrt(8-x^2) is (-2x^2+8)/(sqrt(8-x^2))