What is the derivative of 5xsqrt(64-x^2) ?

The derivative of 5xsqrt(64-x^2) is (5(-2x^2+64))/(sqrt(64-x^2))

What is the first derivative of 5xsqrt(64-x^2) ?

The first derivative of 5xsqrt(64-x^2) is (5(-2x^2+64))/(sqrt(64-x^2))

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\frac{d}{d x} (5 x 64 - x^{2})

\frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

Solution steps

\frac{d}{d x} (5 x 64 - x^{2})

Take the constant out:

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

= 5 \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}

= 5 (\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}}

= 5 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x)

Simplify

5 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x) : \frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

= \frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

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

f (x) = 8 x

\frac{d}{d x} (lo g_{3} (x e^{x}))

y = (x^{3} - 4 x)^{8}, (2, 0)

\frac{d}{d t} (\frac{e ^{t b} - e ^{t a}}{t ( b - a )})

What is the derivative of 5xsqrt(64-x^2) ?
The derivative of 5xsqrt(64-x^2) is (5(-2x^2+64))/(sqrt(64-x^2))
What is the first derivative of 5xsqrt(64-x^2) ?
The first derivative of 5xsqrt(64-x^2) is (5(-2x^2+64))/(sqrt(64-x^2))