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

The derivative of (1-3x^2(x^2-2)^3) is -6(1-3x)(x^2-2)^3+6x(x^2-2)^2(1-3x)^2

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

The first derivative of (1-3x^2(x^2-2)^3) is -6(1-3x)(x^2-2)^3+6x(x^2-2)^2(1-3x)^2

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

- 6 (1 - 3 x) (x^{2} - 2)^{3} + 6 x (x^{2} - 2)^{2} (1 - 3 x)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((1 - 3 x)^{2}) = - 6 (1 - 3 x)

\frac{d}{d x} ((x^{2} - 2)^{3}) = 6 x (x^{2} - 2)^{2}

= (- 6 (1 - 3 x)) (x^{2} - 2)^{3} + 6 x (x^{2} - 2)^{2} (1 - 3 x)^{2}

Simplify

= - 6 (1 - 3 x) (x^{2} - 2)^{3} + 6 x (x^{2} - 2)^{2} (1 - 3 x)^{2}

\frac{\partial}{\partial y} (x y + x)

\frac{d y}{d x} + y = 2

x \to - 3 lim ([\frac{1}{2} x^{2} + 3])

x \to \infty lim (a^{n})

\int sin (x^{4}) d x

What is the derivative of (1-3x^2(x^2-2)^3) ?
The derivative of (1-3x^2(x^2-2)^3) is -6(1-3x)(x^2-2)^3+6x(x^2-2)^2(1-3x)^2
What is the first derivative of (1-3x^2(x^2-2)^3) ?
The first derivative of (1-3x^2(x^2-2)^3) is -6(1-3x)(x^2-2)^3+6x(x^2-2)^2(1-3x)^2