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

The derivative of (1-x(x^2-3)^2) is -5x^4+4x^3+18x^2-12x-9

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

The first derivative of (1-x(x^2-3)^2) is -5x^4+4x^3+18x^2-12x-9

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

- 5 x^{4} + 4 x^{3} + 18 x^{2} - 12 x - 9

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x^{2} - 3)^{2}) = 4 x (x^{2} - 3)

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

Simplify

(- 1) (x^{2} - 3)^{2} + 4 x (x^{2} - 3) (1 - x) : - 5 x^{4} + 4 x^{3} + 18 x^{2} - 12 x - 9

= - 5 x^{4} + 4 x^{3} + 18 x^{2} - 12 x - 9

\int \frac{cos ( t )}{sin ( t )} d t

x^{2} \frac{d y}{d x} + x (x + 2) = e^{x}

n \to 0 lim (\frac{( ( 3 ) ^{n} - 1 )}{n})

x \to 0 + lim (ln (1 - cos (x)) - ln (sin (x)))

\frac{d}{d x} (18 x)

What is the derivative of (1-x(x^2-3)^2) ?
The derivative of (1-x(x^2-3)^2) is -5x^4+4x^3+18x^2-12x-9
What is the first derivative of (1-x(x^2-3)^2) ?
The first derivative of (1-x(x^2-3)^2) is -5x^4+4x^3+18x^2-12x-9