What is the derivative of x^7(x-10)^3 ?

The derivative of x^7(x-10)^3 is 7x^6(x-10)^3+3(x-10)^2x^7

What is the first derivative of x^7(x-10)^3 ?

The first derivative of x^7(x-10)^3 is 7x^6(x-10)^3+3(x-10)^2x^7

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derivative of

x^{7} (x - 10)^{3}

7 x^{6} (x - 10)^{3} + 3 (x - 10)^{2} x^{7}

Solution steps

\frac{d}{d x} (x^{7} (x - 10)^{3})

Apply the Product Rule:

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

f = x^{7}, g = (x - 10)^{3}

= \frac{d}{d x} (x^{7}) (x - 10)^{3} + \frac{d}{d x} ((x - 10)^{3}) x^{7}

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

\frac{d}{d x} ((x - 10)^{3}) = 3 (x - 10)^{2}

= 7 x^{6} (x - 10)^{3} + 3 (x - 10)^{2} x^{7}

What is the derivative of x^7(x-10)^3 ?
The derivative of x^7(x-10)^3 is 7x^6(x-10)^3+3(x-10)^2x^7
What is the first derivative of x^7(x-10)^3 ?
The first derivative of x^7(x-10)^3 is 7x^6(x-10)^3+3(x-10)^2x^7