What is the derivative of x(x-7^2) ?

The derivative of x(x-7^2) is 3x^2-28x+49

What is the first derivative of x(x-7^2) ?

The first derivative of x(x-7^2) is 3x^2-28x+49

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\frac{d}{d x} (x (x - 7)^{2})

3 x^{2} - 28 x + 49

Solution steps

\frac{d}{d x} (x (x - 7)^{2})

Apply the Product Rule:

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

f = x, g = (x - 7)^{2}

= \frac{d x}{d x} (x - 7)^{2} + \frac{d}{d x} ((x - 7)^{2}) x

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

\frac{d}{d x} ((x - 7)^{2}) = 2 (x - 7)

= 1 \cdot (x - 7)^{2} + 2 (x - 7) x

Simplify

1 \cdot (x - 7)^{2} + 2 (x - 7) x : 3 x^{2} - 28 x + 49

= 3 x^{2} - 28 x + 49

What is the derivative of x(x-7^2) ?
The derivative of x(x-7^2) is 3x^2-28x+49
What is the first derivative of x(x-7^2) ?
The first derivative of x(x-7^2) is 3x^2-28x+49