What is the derivative of (7x^4-x+6)(-x^5+1) ?

The derivative of (7x^4-x+6)(-x^5+1) is -63x^8+6x^5-30x^4+28x^3-1

What is the first derivative of (7x^4-x+6)(-x^5+1) ?

The first derivative of (7x^4-x+6)(-x^5+1) is -63x^8+6x^5-30x^4+28x^3-1

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derivative of

(7 x^{4} - x + 6) (- x^{5} + 1)

- 63 x^{8} + 6 x^{5} - 30 x^{4} + 28 x^{3} - 1

Solution steps

\frac{d}{d x} ((7 x^{4} - x + 6) (- x^{5} + 1))

Apply the Product Rule:

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

f = 7 x^{4} - x + 6, g = - x^{5} + 1

= \frac{d}{d x} (7 x^{4} - x + 6) (- x^{5} + 1) + \frac{d}{d x} (- x^{5} + 1) (7 x^{4} - x + 6)

\frac{d}{d x} (7 x^{4} - x + 6) = 28 x^{3} - 1

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

= (28 x^{3} - 1) (- x^{5} + 1) + (- 5 x^{4}) (7 x^{4} - x + 6)

Simplify

(28 x^{3} - 1) (- x^{5} + 1) + (- 5 x^{4}) (7 x^{4} - x + 6) : - 63 x^{8} + 6 x^{5} - 30 x^{4} + 28 x^{3} - 1

= - 63 x^{8} + 6 x^{5} - 30 x^{4} + 28 x^{3} - 1

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What is the derivative of (7x^4-x+6)(-x^5+1) ?
The derivative of (7x^4-x+6)(-x^5+1) is -63x^8+6x^5-30x^4+28x^3-1
What is the first derivative of (7x^4-x+6)(-x^5+1) ?
The first derivative of (7x^4-x+6)(-x^5+1) is -63x^8+6x^5-30x^4+28x^3-1