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Popular >

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

Solution

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

Solution

5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 x (x^{2} - 4) (x - 1) + 1 \cdot (x^{2} - 4)^{2} : 5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

= 5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2-4^2(x-1)) ?
The derivative of (x^2-4^2(x-1)) is 5x^4-4x^3-24x^2+16x+16
What is the first derivative of (x^2-4^2(x-1)) ?
The first derivative of (x^2-4^2(x-1)) is 5x^4-4x^3-24x^2+16x+16