What is the derivative of (x^2-5x+3(4x^3+10x-5)) ?

The derivative of (x^2-5x+3(4x^3+10x-5)) is 20x^4-80x^3+66x^2-110x+55

What is the first derivative of (x^2-5x+3(4x^3+10x-5)) ?

The first derivative of (x^2-5x+3(4x^3+10x-5)) is 20x^4-80x^3+66x^2-110x+55

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\frac{d}{d x} ((x^{2} - 5 x + 3) (4 x^{3} + 10 x - 5))

20 x^{4} - 80 x^{3} + 66 x^{2} - 110 x + 55

Solution steps

\frac{d}{d x} ((x^{2} - 5 x + 3) (4 x^{3} + 10 x - 5))

Apply the Product Rule:

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

f = x^{2} - 5 x + 3, g = 4 x^{3} + 10 x - 5

= \frac{d}{d x} (x^{2} - 5 x + 3) (4 x^{3} + 10 x - 5) + \frac{d}{d x} (4 x^{3} + 10 x - 5) (x^{2} - 5 x + 3)

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

\frac{d}{d x} (4 x^{3} + 10 x - 5) = 12 x^{2} + 10

= (2 x - 5) (4 x^{3} + 10 x - 5) + (12 x^{2} + 10) (x^{2} - 5 x + 3)

Simplify

(2 x - 5) (4 x^{3} + 10 x - 5) + (12 x^{2} + 10) (x^{2} - 5 x + 3) : 20 x^{4} - 80 x^{3} + 66 x^{2} - 110 x + 55

= 20 x^{4} - 80 x^{3} + 66 x^{2} - 110 x + 55

What is the derivative of (x^2-5x+3(4x^3+10x-5)) ?
The derivative of (x^2-5x+3(4x^3+10x-5)) is 20x^4-80x^3+66x^2-110x+55
What is the first derivative of (x^2-5x+3(4x^3+10x-5)) ?
The first derivative of (x^2-5x+3(4x^3+10x-5)) is 20x^4-80x^3+66x^2-110x+55