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Popular >

derivative of x(x-1^4)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Graph

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y^{^{''}} - 4 y^{^{'}} + 4 y = 2 + 8 x - 4 x^{2}

slope ofintercept (-1,-2),(0,5)slope intercept

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Frequently Asked Questions (FAQ)

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