What is the derivative of f(0)=(x^4+3x)(4x^5+4x-2) ?

The derivative of f(0)=(x^4+3x)(4x^5+4x-2) is 36x^8+72x^5+20x^4-8x^3+24x-6

What is the first derivative of f(0)=(x^4+3x)(4x^5+4x-2) ?

The first derivative of f(0)=(x^4+3x)(4x^5+4x-2) is 36x^8+72x^5+20x^4-8x^3+24x-6

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derivative of

f (0) = (x^{4} + 3 x) (4 x^{5} + 4 x - 2)

36 x^{8} + 72 x^{5} + 20 x^{4} - 8 x^{3} + 24 x - 6

Solution steps

\frac{d}{d x} ((x^{4} + 3 x) (4 x^{5} + 4 x - 2))

Apply the Product Rule:

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

f = x^{4} + 3 x, g = 4 x^{5} + 4 x - 2

= \frac{d}{d x} (x^{4} + 3 x) (4 x^{5} + 4 x - 2) + \frac{d}{d x} (4 x^{5} + 4 x - 2) (x^{4} + 3 x)

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

\frac{d}{d x} (4 x^{5} + 4 x - 2) = 20 x^{4} + 4

= (4 x^{3} + 3) (4 x^{5} + 4 x - 2) + (20 x^{4} + 4) (x^{4} + 3 x)

Simplify

(4 x^{3} + 3) (4 x^{5} + 4 x - 2) + (20 x^{4} + 4) (x^{4} + 3 x) : 36 x^{8} + 72 x^{5} + 20 x^{4} - 8 x^{3} + 24 x - 6

= 36 x^{8} + 72 x^{5} + 20 x^{4} - 8 x^{3} + 24 x - 6

What is the derivative of f(0)=(x^4+3x)(4x^5+4x-2) ?
The derivative of f(0)=(x^4+3x)(4x^5+4x-2) is 36x^8+72x^5+20x^4-8x^3+24x-6
What is the first derivative of f(0)=(x^4+3x)(4x^5+4x-2) ?
The first derivative of f(0)=(x^4+3x)(4x^5+4x-2) is 36x^8+72x^5+20x^4-8x^3+24x-6