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Popular >

derivative of x^6(1-x^4)

Solution

\frac{d}{d x} (x^{6} (1 - x)^{4})

Solution

6 x^{5} (1 - x)^{4} - 4 x^{6} (1 - x)^{3}

Solution steps

\frac{d}{d x} (x^{6} (1 - x)^{4})

Apply the Product Rule:

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

f = x^{6}, g = (1 - x)^{4}

= \frac{d}{d x} (x^{6}) (1 - x)^{4} + \frac{d}{d x} ((1 - x)^{4}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} (1 - x)^{4} + (- 4 (1 - x)^{3}) x^{6}

Simplify

= 6 x^{5} (1 - x)^{4} - 4 x^{6} (1 - x)^{3}

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\frac{d y}{d x} = sin (x) y + e^{x}

derivative of y=x^{1-x}derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of x^6(1-x^4) ?
The derivative of x^6(1-x^4) is 6x^5(1-x)^4-4x^6(1-x)^3
What is the first derivative of x^6(1-x^4) ?
The first derivative of x^6(1-x^4) is 6x^5(1-x)^4-4x^6(1-x)^3