What is the derivative of 1/8 x^{2/3}(9x^2-8x-16) ?

The derivative of 1/8 x^{2/3}(9x^2-8x-16) is (9x^2-5x-4)/(3x^{1/3)}

What is the first derivative of 1/8 x^{2/3}(9x^2-8x-16) ?

The first derivative of 1/8 x^{2/3}(9x^2-8x-16) is (9x^2-5x-4)/(3x^{1/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{1}{8} x^{\frac{2}{3}} (9 x^{2} - 8 x - 16)

\frac{9 x ^{2} - 5 x - 4}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (\frac{1}{8} x^{\frac{2}{3}} (9 x^{2} - 8 x - 16))

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (x^{\frac{2}{3}} (9 x^{2} - 8 x - 16))

Apply the Product Rule:

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

f = x^{\frac{2}{3}}, g = 9 x^{2} - 8 x - 16

= \frac{1}{8} (\frac{d}{d x} (x^{\frac{2}{3}}) (9 x^{2} - 8 x - 16) + \frac{d}{d x} (9 x^{2} - 8 x - 16) x^{\frac{2}{3}})

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

\frac{d}{d x} (9 x^{2} - 8 x - 16) = 18 x - 8

= \frac{1}{8} (\frac{2}{3 x ^{\frac{1}{3}}} (9 x^{2} - 8 x - 16) + (18 x - 8) x^{\frac{2}{3}})

Simplify

\frac{1}{8} (\frac{2}{3 x ^{\frac{1}{3}}} (9 x^{2} - 8 x - 16) + (18 x - 8) x^{\frac{2}{3}}) : \frac{9 x ^{2} - 5 x - 4}{3 x ^{\frac{1}{3}}}

= \frac{9 x ^{2} - 5 x - 4}{3 x ^{\frac{1}{3}}}

- cos (x)

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

f (x) = x^{2} + 1

x^{2} - 24 x - 12

f (x) = x^{2} + 3 x

What is the derivative of 1/8 x^{2/3}(9x^2-8x-16) ?
The derivative of 1/8 x^{2/3}(9x^2-8x-16) is (9x^2-5x-4)/(3x^{1/3)}
What is the first derivative of 1/8 x^{2/3}(9x^2-8x-16) ?
The first derivative of 1/8 x^{2/3}(9x^2-8x-16) is (9x^2-5x-4)/(3x^{1/3)}