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Popular >

derivative of f(x)=x^6(x-1)^5

Solution

derivative of

f (x) = x^{6} (x - 1)^{5}

Solution

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

Solution steps

\frac{d}{d x} (x^{6} (x - 1)^{5})

Apply the Product Rule:

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

f = x^{6}, g = (x - 1)^{5}

= \frac{d}{d x} (x^{6}) (x - 1)^{5} + \frac{d}{d x} ((x - 1)^{5}) x^{6}

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

\frac{d}{d x} ((x - 1)^{5}) = 5 (x - 1)^{4}

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

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Frequently Asked Questions (FAQ)

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