What is the derivative of x^3(x-2^5) ?

The derivative of x^3(x-2^5) is 3x^2(x-2)^5+5(x-2)^4x^3

What is the first derivative of x^3(x-2^5) ?

The first derivative of x^3(x-2^5) is 3x^2(x-2)^5+5(x-2)^4x^3

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\frac{d}{d x} (x^{3} (x - 2)^{5})

3 x^{2} (x - 2)^{5} + 5 (x - 2)^{4} x^{3}

Solution steps

\frac{d}{d x} (x^{3} (x - 2)^{5})

Apply the Product Rule:

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

f = x^{3}, g = (x - 2)^{5}

= \frac{d}{d x} (x^{3}) (x - 2)^{5} + \frac{d}{d x} ((x - 2)^{5}) x^{3}

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

\frac{d}{d x} ((x - 2)^{5}) = 5 (x - 2)^{4}

= 3 x^{2} (x - 2)^{5} + 5 (x - 2)^{4} x^{3}

What is the derivative of x^3(x-2^5) ?
The derivative of x^3(x-2^5) is 3x^2(x-2)^5+5(x-2)^4x^3
What is the first derivative of x^3(x-2^5) ?
The first derivative of x^3(x-2^5) is 3x^2(x-2)^5+5(x-2)^4x^3