What is the d/(dy)((x)(x^2-7)) ?

The d/(dy)((x)(x^2-7)) is 3y^2-7

What is the first d/(dy)((x)(x^2-7)) ?

The first d/(dy)((x)(x^2-7)) is 3y^2-7

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\frac{d}{d y} ((y) (y^{2} - 7))

3 y^{2} - 7

Solution steps

\frac{d}{d y} ((y) (y^{2} - 7))

Apply the Product Rule:

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

f = y, g = y^{2} - 7

= \frac{d y}{d y} (y^{2} - 7) + \frac{d}{d y} (y^{2} - 7) y

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

\frac{d}{d y} (y^{2} - 7) = 2 y

= 1 \cdot (y^{2} - 7) + 2 yy

Simplify

1 \cdot (y^{2} - 7) + 2 yy : 3 y^{2} - 7

= 3 y^{2} - 7

- \frac{x ^{3} + 1}{x ( x - 1 ) ^{3}}

(x^{2} - 1) e^{x^{2}}

\frac{( n - 2 ) ( n - 1 )}{2}

\frac{5 ( x - 2 )}{x ^{2}}

2 (\frac{1}{2} - 3)