What is the derivative of ((x^2+2/3)^2) ?

The derivative of ((x^2+2/3)^2) is (4x(x^2+2))/9

What is the first derivative of ((x^2+2/3)^2) ?

The first derivative of ((x^2+2/3)^2) is (4x(x^2+2))/9

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\frac{d}{d x} ((\frac{x ^{2} + 2}{3})^{2})

\frac{4 x ( x ^{2} + 2 )}{9}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 2}{3})^{2})

Apply the chain rule:

2 \cdot \frac{x ^{2} + 2}{3} \frac{d}{d x} (\frac{x ^{2} + 2}{3})

= 2 \cdot \frac{x ^{2} + 2}{3} \frac{d}{d x} (\frac{x ^{2} + 2}{3})

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

= 2 \cdot \frac{x ^{2} + 2}{3} \cdot \frac{2 x}{3}

Simplify

2 \cdot \frac{x ^{2} + 2}{3} \cdot \frac{2 x}{3} : \frac{4 x ( x ^{2} + 2 )}{9}

= \frac{4 x ( x ^{2} + 2 )}{9}

(3, 2), (- 3, - 2)

A e^{x}

f (x) = sec (x) tan (x)

\frac{d}{d x} (- 4 cos (x) + sin (x))

f (x) = \frac{x}{( 4 x - 3 ) ^{8}}, at x = 1

What is the derivative of ((x^2+2/3)^2) ?
The derivative of ((x^2+2/3)^2) is (4x(x^2+2))/9
What is the first derivative of ((x^2+2/3)^2) ?
The first derivative of ((x^2+2/3)^2) is (4x(x^2+2))/9