What is the derivative of f(x)=(x+x^4)(-x-1) ?

The derivative of f(x)=(x+x^4)(-x-1) is -5x^4-4x^3-2x-1

What is the first derivative of f(x)=(x+x^4)(-x-1) ?

The first derivative of f(x)=(x+x^4)(-x-1) is -5x^4-4x^3-2x-1

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derivative of

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

- 5 x^{4} - 4 x^{3} - 2 x - 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (- x - 1) = - 1

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

Simplify

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

= - 5 x^{4} - 4 x^{3} - 2 x - 1

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