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

The derivative of ((-3x+1^4-5)^3) is 3(81x^4-108x^3+54x^2-12x-4)^2(324x^3-324x^2+108x-12)

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

The first derivative of ((-3x+1^4-5)^3) is 3(81x^4-108x^3+54x^2-12x-4)^2(324x^3-324x^2+108x-12)

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

3 (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)^{2} (324 x^{3} - 324 x^{2} + 108 x - 12)

Solution steps

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

Simplify

((- 3 x + 1)^{4} - 5)^{3} : (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)^{3}

= \frac{d}{d x} ((81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)^{3})

Apply the chain rule:

3 (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)^{2} \frac{d}{d x} (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)

= 3 (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)^{2} \frac{d}{d x} (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)

\frac{d}{d x} (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4) = 324 x^{3} - 324 x^{2} + 108 x - 12

= 3 (81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x - 4)^{2} (324 x^{3} - 324 x^{2} + 108 x - 12)

What is the derivative of ((-3x+1^4-5)^3) ?
The derivative of ((-3x+1^4-5)^3) is 3(81x^4-108x^3+54x^2-12x-4)^2(324x^3-324x^2+108x-12)
What is the first derivative of ((-3x+1^4-5)^3) ?
The first derivative of ((-3x+1^4-5)^3) is 3(81x^4-108x^3+54x^2-12x-4)^2(324x^3-324x^2+108x-12)