What is the derivative of sqrt((x(a-x^2)/(3a))) ?

The derivative of sqrt((x(a-x^2)/(3a))) is -(3x-a)/(2sqrt(3)\sqrt{a)sqrt(x)}

What is the first derivative of sqrt((x(a-x^2)/(3a))) ?

The first derivative of sqrt((x(a-x^2)/(3a))) is -(3x-a)/(2sqrt(3)\sqrt{a)sqrt(x)}

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\frac{d}{d x} \frac{x ( a - x ) ^{2}}{3 a}

- \frac{3 x - a}{2 3 a x}

Solution steps

\frac{d}{d x} \frac{x ( a - x ) ^{2}}{3 a}

Apply the chain rule:

\frac{1}{2 \frac{x ( a - x ) ^{2}}{3 a}} \frac{d}{d x} (\frac{x ( a - x ) ^{2}}{3 a})

= \frac{1}{2 \frac{x ( a - x ) ^{2}}{3 a}} \frac{d}{d x} (\frac{x ( a - x ) ^{2}}{3 a})

\frac{d}{d x} (\frac{x ( a - x ) ^{2}}{3 a}) = \frac{3 x ^{2} - 4 a x + a ^{2}}{3 a}

= \frac{1}{2 \frac{x ( a - x ) ^{2}}{3 a}} \cdot \frac{3 x ^{2} - 4 a x + a ^{2}}{3 a}

Simplify

\frac{1}{2 \frac{x ( a - x ) ^{2}}{3 a}} \cdot \frac{3 x ^{2} - 4 a x + a ^{2}}{3 a} : - \frac{3 x - a}{2 3 a x}

= - \frac{3 x - a}{2 3 a x}

\frac{5 ( 1 - 4 ln ( x ) )}{2 x ^{5}}

\int sin^{4} (5 θ) cos^{5} (5 θ) d θ

f (x) = sin (x)

\frac{d y}{d x}, (x - 1)^{2} + (y + 4)^{2} = 25

y^{^{'}} - y = 2 x e^{2 x}, y (0) = 1

What is the derivative of sqrt((x(a-x^2)/(3a))) ?
The derivative of sqrt((x(a-x^2)/(3a))) is -(3x-a)/(2sqrt(3)\sqrt{a)sqrt(x)}
What is the first derivative of sqrt((x(a-x^2)/(3a))) ?
The first derivative of sqrt((x(a-x^2)/(3a))) is -(3x-a)/(2sqrt(3)\sqrt{a)sqrt(x)}