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

The derivative of x(x-1^2(x-2)^3) is 3x^2(x-2)^3-4x(x-2)^3+(x-2)^3+3x(x-2)^2(x-1)^2

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

The first derivative of x(x-1^2(x-2)^3) is 3x^2(x-2)^3-4x(x-2)^3+(x-2)^3+3x(x-2)^2(x-1)^2

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int π^{π} d x

y = x (3 x + 4)^{5}

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

\frac{\partial}{\partial x} (\frac{9 x z}{x + y})

\int \frac{x ^{2} - 6 x - 17}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

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