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

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