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

The derivative of y=(2x+1)(x-2)^3 is 2(x-2)^3+3(x-2)^2(2x+1)

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

The first derivative of y=(2x+1)(x-2)^3 is 2(x-2)^3+3(x-2)^2(2x+1)

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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