What is the derivative of y=(5-x^2)(x^3-3x+2) ?

The derivative of y=(5-x^2)(x^3-3x+2) is -5x^4+24x^2-4x-15

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

The first derivative of y=(5-x^2)(x^3-3x+2) is -5x^4+24x^2-4x-15

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derivative of

y = (5 - x^{2}) (x^{3} - 3 x + 2)

- 5 x^{4} + 24 x^{2} - 4 x - 15

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- 2 x) (x^{3} - 3 x + 2) + (3 x^{2} - 3) (5 - x^{2}) : - 5 x^{4} + 24 x^{2} - 4 x - 15

= - 5 x^{4} + 24 x^{2} - 4 x - 15

\int_{1}^{2} 2 x^{2} d x

y = cos (5 x)

\int_{0}^{\frac{1}{3}} arcsin (3 y) d y

x \to π lim (\frac{3 x + 1}{1 - x})

\frac{d}{d x} ((ln (3 x))^{2})

What is the derivative of y=(5-x^2)(x^3-3x+2) ?
The derivative of y=(5-x^2)(x^3-3x+2) is -5x^4+24x^2-4x-15
What is the first derivative of y=(5-x^2)(x^3-3x+2) ?
The first derivative of y=(5-x^2)(x^3-3x+2) is -5x^4+24x^2-4x-15