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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{1}{- x ^{2} - 10 x - 24} d x

x \to 3 lim (1 - x - x^{2})

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}})

\int_{1}^{2} \frac{x - 1}{x} d x

\int e^{x} \cdot 2 x d x

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