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Popular >

derivative of (x^2-1^4(2-3x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{4}) = 8 x (x^{2} - 1)^{3}

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

= 8 x (x^{2} - 1)^{3} (2 - 3 x) + (- 3) (x^{2} - 1)^{4}

Simplify

= 8 x (x^{2} - 1)^{3} (2 - 3 x) - 3 (x^{2} - 1)^{4}

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2-1^4(2-3x)) ?
The derivative of (x^2-1^4(2-3x)) is 8x(x^2-1)^3(2-3x)-3(x^2-1)^4
What is the first derivative of (x^2-1^4(2-3x)) ?
The first derivative of (x^2-1^4(2-3x)) is 8x(x^2-1)^3(2-3x)-3(x^2-1)^4