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

The derivative of y=x^2(x^3-1)^5 is 2x(x^3-1)^5+15x^4(x^3-1)^4

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

The first derivative of y=x^2(x^3-1)^5 is 2x(x^3-1)^5+15x^4(x^3-1)^4

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derivative of

y = x^{2} (x^{3} - 1)^{5}

2 x (x^{3} - 1)^{5} + 15 x^{4} (x^{3} - 1)^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x^{3} - 1)^{5}) = 15 x^{2} (x^{3} - 1)^{4}

= 2 x (x^{3} - 1)^{5} + 15 x^{2} (x^{3} - 1)^{4} x^{2}

15 x^{2} (x^{3} - 1)^{4} x^{2} = 15 x^{4} (x^{3} - 1)^{4}

= 2 x (x^{3} - 1)^{5} + 15 x^{4} (x^{3} - 1)^{4}

What is the derivative of y=x^2(x^3-1)^5 ?
The derivative of y=x^2(x^3-1)^5 is 2x(x^3-1)^5+15x^4(x^3-1)^4
What is the first derivative of y=x^2(x^3-1)^5 ?
The first derivative of y=x^2(x^3-1)^5 is 2x(x^3-1)^5+15x^4(x^3-1)^4