What is the derivative of (3x-1(x-2)^4) ?

The derivative of (3x-1(x-2)^4) is 3(x-2)^4+4(x-2)^3(3x-1)

What is the first derivative of (3x-1(x-2)^4) ?

The first derivative of (3x-1(x-2)^4) is 3(x-2)^4+4(x-2)^3(3x-1)

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\frac{d}{d x} ((3 x - 1) (x - 2)^{4})

3 (x - 2)^{4} + 4 (x - 2)^{3} (3 x - 1)

Solution steps

\frac{d}{d x} ((3 x - 1) (x - 2)^{4})

Apply the Product Rule:

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

f = 3 x - 1, g = (x - 2)^{4}

= \frac{d}{d x} (3 x - 1) (x - 2)^{4} + \frac{d}{d x} ((x - 2)^{4}) (3 x - 1)

\frac{d}{d x} (3 x - 1) = 3

\frac{d}{d x} ((x - 2)^{4}) = 4 (x - 2)^{3}

= 3 (x - 2)^{4} + 4 (x - 2)^{3} (3 x - 1)

What is the derivative of (3x-1(x-2)^4) ?
The derivative of (3x-1(x-2)^4) is 3(x-2)^4+4(x-2)^3(3x-1)
What is the first derivative of (3x-1(x-2)^4) ?
The first derivative of (3x-1(x-2)^4) is 3(x-2)^4+4(x-2)^3(3x-1)