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

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

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

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

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derivative of

f (z) = (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

\int (4 - 2 x)^{2} d x

x \to - 8 lim (9 x + 10)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = \frac{e ^{x}}{x}

\int x^{3} + 2 x + 3 d x

\frac{( d x )}{( d y )} = \frac{8 - ( 2 x )}{( 100 + 2 y )}

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