What is the d/(dy)((x)(cos(x)y+3xy^2)) ?

The d/(dy)((x)(cos(x)y+3xy^2)) is x(cos(x)+6xy)

What is the first d/(dy)((x)(cos(x)y+3xy^2)) ?

The first d/(dy)((x)(cos(x)y+3xy^2)) is x(cos(x)+6xy)

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\frac{d}{d y} ((x) (cos (x) y + 3 x y^{2}))

x (cos (x) + 6 x y)

Solution steps

\frac{d}{d y} ((x) (cos (x) y + 3 x y^{2}))

Treat

x

as a constant

Take the constant out:

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

= x \frac{d}{d y} (cos (x) y + 3 x y^{2})

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d y} (cos (x) y) + \frac{d}{d y} (3 x y^{2}))

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

\frac{d}{d y} (3 x y^{2}) = 6 x y

= x (cos (x) + 6 x y)

(- 43 + 4 i)^{5}

2 (x + 2 - x^{2})

\frac{1}{12} (cos (8 t) - 8 sin (8 t))

\frac{2 x}{( x ^{2} + 25 ) ( x - 1 )}

\frac{1}{( 6 + x ) ^{3}}

What is the d/(dy)((x)(cos(x)y+3xy^2)) ?
The d/(dy)((x)(cos(x)y+3xy^2)) is x(cos(x)+6xy)
What is the first d/(dy)((x)(cos(x)y+3xy^2)) ?
The first d/(dy)((x)(cos(x)y+3xy^2)) is x(cos(x)+6xy)