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

The derivative of (2x^2+1)(x-3)^2 is 8x^3-36x^2+38x-6

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

The first derivative of (2x^2+1)(x-3)^2 is 8x^3-36x^2+38x-6

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derivative of

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

8 x^{3} - 36 x^{2} + 38 x - 6

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

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

Simplify

4 x (x - 3)^{2} + 2 (x - 3) (2 x^{2} + 1) : 8 x^{3} - 36 x^{2} + 38 x - 6

= 8 x^{3} - 36 x^{2} + 38 x - 6

What is the derivative of (2x^2+1)(x-3)^2 ?
The derivative of (2x^2+1)(x-3)^2 is 8x^3-36x^2+38x-6
What is the first derivative of (2x^2+1)(x-3)^2 ?
The first derivative of (2x^2+1)(x-3)^2 is 8x^3-36x^2+38x-6