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Popular >

derivative of (x+1^3(1-x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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