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Popular >

derivative of (x-1(x-2)(2-x^2))

Solution

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

Solution

- 4 x^{3} + 9 x^{2} - 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x - 2) (2 - x^{2}) + (2 - 3 x^{2} + 4 x) (x - 1) : - 4 x^{3} + 9 x^{2} - 6

= - 4 x^{3} + 9 x^{2} - 6

Popular Examples

derivative of 3/(sqrt(6t+3))derivative of

\frac{3}{6 t + 3}

f^'(t)=(8t)/(8+sqrt(t))

f^{^{'}} (t) = \frac{8 t}{8 + t}

derivative of f(x)=(2x^2-1)^{1/2}derivative of

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

y^{''}+8y^'+65y=0,y(0)=0,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 65 y = 0, y (0) = 0, y^{^{'}} (0) = 0

limit as x approaches-2 of x^2-2x^2+2x+3

x \to - 2 lim (x^{2} - 2 x^{2} + 2 x + 3)

Frequently Asked Questions (FAQ)

What is the derivative of (x-1(x-2)(2-x^2)) ?
The derivative of (x-1(x-2)(2-x^2)) is -4x^3+9x^2-6
What is the first derivative of (x-1(x-2)(2-x^2)) ?
The first derivative of (x-1(x-2)(2-x^2)) is -4x^3+9x^2-6