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

The derivative of (2x^4-x+1(-x^5+4)) is -18x^8+6x^5-5x^4+32x^3-4

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

The first derivative of (2x^4-x+1(-x^5+4)) is -18x^8+6x^5-5x^4+32x^3-4

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

- 18 x^{8} + 6 x^{5} - 5 x^{4} + 32 x^{3} - 4

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2 x^{4} - x + 1) = 8 x^{3} - 1

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

= (8 x^{3} - 1) (- x^{5} + 4) + (- 5 x^{4}) (2 x^{4} - x + 1)

Simplify

(8 x^{3} - 1) (- x^{5} + 4) + (- 5 x^{4}) (2 x^{4} - x + 1) : - 18 x^{8} + 6 x^{5} - 5 x^{4} + 32 x^{3} - 4

= - 18 x^{8} + 6 x^{5} - 5 x^{4} + 32 x^{3} - 4

What is the derivative of (2x^4-x+1(-x^5+4)) ?
The derivative of (2x^4-x+1(-x^5+4)) is -18x^8+6x^5-5x^4+32x^3-4
What is the first derivative of (2x^4-x+1(-x^5+4)) ?
The first derivative of (2x^4-x+1(-x^5+4)) is -18x^8+6x^5-5x^4+32x^3-4