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Popular >

derivative of (4x+1(1-x)^3)

Solution

\frac{d}{d x} ((4 x + 1) (1 - x)^{3})

Solution

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

Solution steps

\frac{d}{d x} ((4 x + 1) (1 - x)^{3})

Apply the Product Rule:

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

f = 4 x + 1, g = (1 - x)^{3}

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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