What is the derivative of (5x-4(2x^3-x^2+1)) ?

The derivative of (5x-4(2x^3-x^2+1)) is 40x^3-39x^2+8x+5

What is the first derivative of (5x-4(2x^3-x^2+1)) ?

The first derivative of (5x-4(2x^3-x^2+1)) is 40x^3-39x^2+8x+5

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\frac{d}{d x} ((5 x - 4) (2 x^{3} - x^{2} + 1))

40 x^{3} - 39 x^{2} + 8 x + 5

Solution steps

\frac{d}{d x} ((5 x - 4) (2 x^{3} - x^{2} + 1))

Apply the Product Rule:

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

f = 5 x - 4, g = 2 x^{3} - x^{2} + 1

= \frac{d}{d x} (5 x - 4) (2 x^{3} - x^{2} + 1) + \frac{d}{d x} (2 x^{3} - x^{2} + 1) (5 x - 4)

\frac{d}{d x} (5 x - 4) = 5

\frac{d}{d x} (2 x^{3} - x^{2} + 1) = 6 x^{2} - 2 x

= 5 (2 x^{3} - x^{2} + 1) + (6 x^{2} - 2 x) (5 x - 4)

Simplify

5 (2 x^{3} - x^{2} + 1) + (6 x^{2} - 2 x) (5 x - 4) : 40 x^{3} - 39 x^{2} + 8 x + 5

= 40 x^{3} - 39 x^{2} + 8 x + 5

f (x) = \frac{1}{4 + 3 x}, (1, \frac{1}{7})

e^{9 x}

f (x) = 2 x^{2} - 4 x + 1

\int \frac{1}{x ^{\frac{5}{8}} - x ^{\frac{1}{8}}} d x

\int 31 arctan (x) d x

What is the derivative of (5x-4(2x^3-x^2+1)) ?
The derivative of (5x-4(2x^3-x^2+1)) is 40x^3-39x^2+8x+5
What is the first derivative of (5x-4(2x^3-x^2+1)) ?
The first derivative of (5x-4(2x^3-x^2+1)) is 40x^3-39x^2+8x+5