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

The derivative of y=(5x^2+x)(x-x^2) is -20x^3+12x^2+2x

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

The first derivative of y=(5x^2+x)(x-x^2) is -20x^3+12x^2+2x

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derivative of

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

- 20 x^{3} + 12 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 x^{2} + x) = 10 x + 1

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

= (10 x + 1) (x - x^{2}) + (1 - 2 x) (5 x^{2} + x)

Simplify

(10 x + 1) (x - x^{2}) + (1 - 2 x) (5 x^{2} + x) : - 20 x^{3} + 12 x^{2} + 2 x

= - 20 x^{3} + 12 x^{2} + 2 x

What is the derivative of y=(5x^2+x)(x-x^2) ?
The derivative of y=(5x^2+x)(x-x^2) is -20x^3+12x^2+2x
What is the first derivative of y=(5x^2+x)(x-x^2) ?
The first derivative of y=(5x^2+x)(x-x^2) is -20x^3+12x^2+2x