What is the d/(dy)((x)(xy+sin(xy)+x)) ?

The d/(dy)((x)(xy+sin(xy)+x)) is x(x+xcos(xy))

What is the first d/(dy)((x)(xy+sin(xy)+x)) ?

The first d/(dy)((x)(xy+sin(xy)+x)) is x(x+xcos(xy))

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\frac{d}{d y} ((x) (x y + sin (x y) + x))

x (x + x cos (x y))

Solution steps

\frac{d}{d y} ((x) (x y + sin (x y) + x))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{d}{d y} (x y + sin (x y) + x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{d}{d y} (x y) + \frac{d}{d y} (sin (x y)) + \frac{d x}{d y})

\frac{d}{d y} (x y) = x

\frac{d}{d y} (sin (x y)) = cos (x y) x

\frac{d x}{d y} = 0

= x (x + cos (x y) x + 0)

Simplify

= x (x + x cos (x y))

\frac{( 4 x - 3 ) ( x + 2 )}{8 x + 6}

1 (- 4 x + 2 y = 6)

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

\frac{5 ( 3 30 - 10 )}{34}

\frac{689}{96 ( 2 x - 1 )}

What is the d/(dy)((x)(xy+sin(xy)+x)) ?
The d/(dy)((x)(xy+sin(xy)+x)) is x(x+xcos(xy))
What is the first d/(dy)((x)(xy+sin(xy)+x)) ?
The first d/(dy)((x)(xy+sin(xy)+x)) is x(x+xcos(xy))