What is the derivative of 1/8 xsqrt(64-x^2) ?

The derivative of 1/8 xsqrt(64-x^2) is (32-x^2)/(4sqrt(-x^2+64))

What is the first derivative of 1/8 xsqrt(64-x^2) ?

The first derivative of 1/8 xsqrt(64-x^2) is (32-x^2)/(4sqrt(-x^2+64))

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\frac{d}{d x} (\frac{1}{8} x 64 - x^{2})

\frac{32 - x ^{2}}{4 - x ^{2} + 64}

Solution steps

\frac{d}{d x} (\frac{1}{8} x 64 - x^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (x 64 - x^{2})

Apply the Product Rule:

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

f = x, g = 64 - x^{2}

= \frac{1}{8} (\frac{d x}{d x} 64 - x^{2} + \frac{d}{d x} (64 - x^{2}) x)

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

\frac{d}{d x} (64 - x^{2}) = - \frac{x}{64 - x ^{2}}

= \frac{1}{8} (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x)

Simplify

\frac{1}{8} (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x) : \frac{32 - x ^{2}}{4 - x ^{2} + 64}

= \frac{32 - x ^{2}}{4 - x ^{2} + 64}

(5, - 4), (4, 7)

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What is the derivative of 1/8 xsqrt(64-x^2) ?
The derivative of 1/8 xsqrt(64-x^2) is (32-x^2)/(4sqrt(-x^2+64))
What is the first derivative of 1/8 xsqrt(64-x^2) ?
The first derivative of 1/8 xsqrt(64-x^2) is (32-x^2)/(4sqrt(-x^2+64))