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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int \frac{y ^{2}}{y ^{6} + 1} d y

n = 1 \sum \infty 7 (- 4)^{n - 1}

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

5 x, x^{2}

x \to 0 lim (\frac{x}{x + 2})

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