What is the derivative of (x-a^3(x-b)) ?

The derivative of (x-a^3(x-b)) is 3(x-a)^2(x-b)+(x-a)^3

What is the first derivative of (x-a^3(x-b)) ?

The first derivative of (x-a^3(x-b)) is 3(x-a)^2(x-b)+(x-a)^3

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\frac{d}{d x} ((x - a)^{3} (x - b))

3 (x - a)^{2} (x - b) + (x - a)^{3}

Solution steps

\frac{d}{d x} ((x - a)^{3} (x - b))

Apply the Product Rule:

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

f = (x - a)^{3}, g = x - b

= \frac{d}{d x} ((x - a)^{3}) (x - b) + \frac{d}{d x} (x - b) (x - a)^{3}

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

\frac{d}{d x} (x - b) = 1

= 3 (x - a)^{2} (x - b) + 1 \cdot (x - a)^{3}

Simplify

= 3 (x - a)^{2} (x - b) + (x - a)^{3}

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