What is the derivative of (9z^4+3z^2+1)(3z^3-z) ?

The derivative of (9z^4+3z^2+1)(3z^3-z) is 189z^6-1

What is the first derivative of (9z^4+3z^2+1)(3z^3-z) ?

The first derivative of (9z^4+3z^2+1)(3z^3-z) is 189z^6-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z)

189 z^{6} - 1

Solution steps

\frac{d}{d z} ((9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z))

Apply the Product Rule:

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

f = 9 z^{4} + 3 z^{2} + 1, g = 3 z^{3} - z

= \frac{d}{d z} (9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z) + \frac{d}{d z} (3 z^{3} - z) (9 z^{4} + 3 z^{2} + 1)

\frac{d}{d z} (9 z^{4} + 3 z^{2} + 1) = 36 z^{3} + 6 z

\frac{d}{d z} (3 z^{3} - z) = 9 z^{2} - 1

= (36 z^{3} + 6 z) (3 z^{3} - z) + (9 z^{2} - 1) (9 z^{4} + 3 z^{2} + 1)

Simplify

(36 z^{3} + 6 z) (3 z^{3} - z) + (9 z^{2} - 1) (9 z^{4} + 3 z^{2} + 1) : 189 z^{6} - 1

= 189 z^{6} - 1

y^{^{'}} = 8 x + y, y (0) = 4

\frac{\partial}{\partial t} (a e^{k x + wt})

\int f (x) g (x) d x

x \to \infty lim (x - 8)

\int \frac{5}{4 + x} d x

What is the derivative of (9z^4+3z^2+1)(3z^3-z) ?
The derivative of (9z^4+3z^2+1)(3z^3-z) is 189z^6-1
What is the first derivative of (9z^4+3z^2+1)(3z^3-z) ?
The first derivative of (9z^4+3z^2+1)(3z^3-z) is 189z^6-1