What is the derivative of y=(3-x^2)(x^3-x+1) ?

The derivative of y=(3-x^2)(x^3-x+1) is -5x^4+12x^2-2x-3

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

The first derivative of y=(3-x^2)(x^3-x+1) is -5x^4+12x^2-2x-3

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derivative of

y = (3 - x^{2}) (x^{3} - x + 1)

- 5 x^{4} + 12 x^{2} - 2 x - 3

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- 2 x) (x^{3} - x + 1) + (3 x^{2} - 1) (3 - x^{2}) : - 5 x^{4} + 12 x^{2} - 2 x - 3

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

sec^{2} (x) tan (x)

(x^{3} - 1)^{3}

\frac{sin ( x )}{x ^{2}}

e^{2} + (sec (x) x)

\frac{d}{dd} (10 d)

What is the derivative of y=(3-x^2)(x^3-x+1) ?
The derivative of y=(3-x^2)(x^3-x+1) is -5x^4+12x^2-2x-3
What is the first derivative of y=(3-x^2)(x^3-x+1) ?
The first derivative of y=(3-x^2)(x^3-x+1) is -5x^4+12x^2-2x-3