What is the derivative of x(x-4^2) ?

The derivative of x(x-4^2) is 3x^2-16x+16

What is the first derivative of x(x-4^2) ?

The first derivative of x(x-4^2) is 3x^2-16x+16

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

3 x^{2} - 16 x + 16

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 4)^{2}

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

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

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

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

Simplify

1 \cdot (x - 4)^{2} + 2 (x - 4) x : 3 x^{2} - 16 x + 16

= 3 x^{2} - 16 x + 16

2 x^{2} + 3 x, at x = - 3

\int \frac{cos ( x )}{8 + sin ( x )} d x

x \to 0 lim ((1 + 8 x)^{\frac{3}{x}})

\int (2 x + 6) 5 d x

\int \frac{1}{x ^{6}} d x

What is the derivative of x(x-4^2) ?
The derivative of x(x-4^2) is 3x^2-16x+16
What is the first derivative of x(x-4^2) ?
The first derivative of x(x-4^2) is 3x^2-16x+16