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Popular >

derivative of x^7(x-12^5)

Solution

\frac{d}{d x} (x^{7} (x - 12)^{5})

Solution

7 x^{6} (x - 12)^{5} + 5 (x - 12)^{4} x^{7}

Solution steps

\frac{d}{d x} (x^{7} (x - 12)^{5})

Apply the Product Rule:

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

f = x^{7}, g = (x - 12)^{5}

= \frac{d}{d x} (x^{7}) (x - 12)^{5} + \frac{d}{d x} ((x - 12)^{5}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} ((x - 12)^{5}) = 5 (x - 12)^{4}

= 7 x^{6} (x - 12)^{5} + 5 (x - 12)^{4} x^{7}

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Frequently Asked Questions (FAQ)

What is the derivative of x^7(x-12^5) ?
The derivative of x^7(x-12^5) is 7x^6(x-12)^5+5(x-12)^4x^7
What is the first derivative of x^7(x-12^5) ?
The first derivative of x^7(x-12^5) is 7x^6(x-12)^5+5(x-12)^4x^7