What is the first d/(dy)((x)(3x+5y)) ?

The first d/(dy)((x)(3x+5y)) is 5x

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d/(dy)((x)(3x+5y))

\frac{d}{d y} ((x) (3 x + 5 y))

5 x

Solution steps

\frac{d}{d y} ((x) (3 x + 5 y))

Treat

x

as a constant

Take the constant out:

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

= x \frac{d}{d y} (3 x + 5 y)

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d y} (3 x) + \frac{d}{d y} (5 y))

\frac{d}{d y} (3 x) = 0

\frac{d}{d y} (5 y) = 5

= x (0 + 5)

Simplify

= 5 x

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

\frac{4 ( x + 3 )}{x - 4}

\frac{e ^{t}}{2 ( t ^{2} + 5 t )}

e^{90 (x + y)}

π (2 - 2)