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

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

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

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

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derivative of

y = 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}}

x - 2 sin (x)

y = x^{3}, y = 1, x = 2, x = 2

\int \frac{1}{3 x - 5} d x

x \to 0 - lim (\frac{3}{x} - \frac{3}{∣ x ∣})

\frac{d}{d x} (150 + \frac{1}{x} + x^{2})

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