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Popular >

derivative of (x-1)^2(2x+1)^4

Solution

derivative of

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

Solution

2 (x - 1) (2 x + 1)^{4} + 8 (2 x + 1)^{3} (x - 1)^{2}

Solution steps

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

Apply the Product Rule:

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

f = (x - 1)^{2}, g = (2 x + 1)^{4}

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

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

\frac{d}{d x} ((2 x + 1)^{4}) = 8 (2 x + 1)^{3}

= 2 (x - 1) (2 x + 1)^{4} + 8 (2 x + 1)^{3} (x - 1)^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x-1)^2(2x+1)^4 ?
The derivative of (x-1)^2(2x+1)^4 is 2(x-1)(2x+1)^4+8(2x+1)^3(x-1)^2
What is the first derivative of (x-1)^2(2x+1)^4 ?
The first derivative of (x-1)^2(2x+1)^4 is 2(x-1)(2x+1)^4+8(2x+1)^3(x-1)^2