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

The derivative of y=(2x-1)^5(1-x^4)^4 is 10(2x-1)^4(1-x^4)^4-16x^3(1-x^4)^3(2x-1)^5

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

The first derivative of y=(2x-1)^5(1-x^4)^4 is 10(2x-1)^4(1-x^4)^4-16x^3(1-x^4)^3(2x-1)^5

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derivative of

y = (2 x - 1)^{5} (1 - x^{4})^{4}

10 (2 x - 1)^{4} (1 - x^{4})^{4} - 16 x^{3} (1 - x^{4})^{3} (2 x - 1)^{5}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((2 x - 1)^{5}) = 10 (2 x - 1)^{4}

\frac{d}{d x} ((1 - x^{4})^{4}) = - 16 x^{3} (1 - x^{4})^{3}

= 10 (2 x - 1)^{4} (1 - x^{4})^{4} + (- 16 x^{3} (1 - x^{4})^{3}) (2 x - 1)^{5}

Simplify

= 10 (2 x - 1)^{4} (1 - x^{4})^{4} - 16 x^{3} (1 - x^{4})^{3} (2 x - 1)^{5}

What is the derivative of y=(2x-1)^5(1-x^4)^4 ?
The derivative of y=(2x-1)^5(1-x^4)^4 is 10(2x-1)^4(1-x^4)^4-16x^3(1-x^4)^3(2x-1)^5
What is the first derivative of y=(2x-1)^5(1-x^4)^4 ?
The first derivative of y=(2x-1)^5(1-x^4)^4 is 10(2x-1)^4(1-x^4)^4-16x^3(1-x^4)^3(2x-1)^5