What is the derivative of (3x-3)^2(1-5x)^4 ?

The derivative of (3x-3)^2(1-5x)^4 is 6(3x-3)(1-5x)^4-20(1-5x)^3(3x-3)^2

What is the first derivative of (3x-3)^2(1-5x)^4 ?

The first derivative of (3x-3)^2(1-5x)^4 is 6(3x-3)(1-5x)^4-20(1-5x)^3(3x-3)^2

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derivative of

(3 x - 3)^{2} (1 - 5 x)^{4}

6 (3 x - 3) (1 - 5 x)^{4} - 20 (1 - 5 x)^{3} (3 x - 3)^{2}

Solution steps

\frac{d}{d x} ((3 x - 3)^{2} (1 - 5 x)^{4})

Apply the Product Rule:

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

f = (3 x - 3)^{2}, g = (1 - 5 x)^{4}

= \frac{d}{d x} ((3 x - 3)^{2}) (1 - 5 x)^{4} + \frac{d}{d x} ((1 - 5 x)^{4}) (3 x - 3)^{2}

\frac{d}{d x} ((3 x - 3)^{2}) = 6 (3 x - 3)

\frac{d}{d x} ((1 - 5 x)^{4}) = - 20 (1 - 5 x)^{3}

= 6 (3 x - 3) (1 - 5 x)^{4} + (- 20 (1 - 5 x)^{3}) (3 x - 3)^{2}

Simplify

= 6 (3 x - 3) (1 - 5 x)^{4} - 20 (1 - 5 x)^{3} (3 x - 3)^{2}

What is the derivative of (3x-3)^2(1-5x)^4 ?
The derivative of (3x-3)^2(1-5x)^4 is 6(3x-3)(1-5x)^4-20(1-5x)^3(3x-3)^2
What is the first derivative of (3x-3)^2(1-5x)^4 ?
The first derivative of (3x-3)^2(1-5x)^4 is 6(3x-3)(1-5x)^4-20(1-5x)^3(3x-3)^2