What is the d/(dy)((x)((x^2-1)^4)) ?

The d/(dy)((x)((x^2-1)^4)) is (y^2-1)^4+8y^2(y^2-1)^3

What is the first d/(dy)((x)((x^2-1)^4)) ?

The first d/(dy)((x)((x^2-1)^4)) is (y^2-1)^4+8y^2(y^2-1)^3

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d y}{d y} = 1

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

= 1 \cdot (y^{2} - 1)^{4} + 8 y (y^{2} - 1)^{3} y

Simplify

1 \cdot (y^{2} - 1)^{4} + 8 y (y^{2} - 1)^{3} y : (y^{2} - 1)^{4} + 8 y^{2} (y^{2} - 1)^{3}

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

(\frac{2 x ^{4}}{y} - \frac{y ^{2}}{x})^{10}

(r - r cos (θ))^{2}

2 (32 + 2)

7 (1 + 6 sin (θ))^{2}

\frac{( 10 - 3 x ) ( x + 1 )}{5}

What is the d/(dy)((x)((x^2-1)^4)) ?
The d/(dy)((x)((x^2-1)^4)) is (y^2-1)^4+8y^2(y^2-1)^3
What is the first d/(dy)((x)((x^2-1)^4)) ?
The first d/(dy)((x)((x^2-1)^4)) is (y^2-1)^4+8y^2(y^2-1)^3