What is the d/(dy)(ln(y+2)*e^2xy) ?

The d/(dy)(ln(y+2)*e^2xy) is e^2x(y/(y+2)+ln(y+2))

What is the first d/(dy)(ln(y+2)*e^2xy) ?

The first d/(dy)(ln(y+2)*e^2xy) is e^2x(y/(y+2)+ln(y+2))

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\frac{d}{d y} (ln (y + 2) \cdot e^{2} x y)

e^{2} x (\frac{y}{y + 2} + ln (y + 2))

Solution steps

\frac{d}{d y} (ln (y + 2) e^{2} x y)

Treat

x

as a constant

Take the constant out:

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

= e^{2} x \frac{d}{d y} (ln (y + 2) y)

Apply the Product Rule:

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

f = ln (y + 2), g = y

= e^{2} x (\frac{d}{d y} (ln (y + 2)) y + \frac{d y}{d y} ln (y + 2))

\frac{d}{d y} (ln (y + 2)) = \frac{1}{y + 2}

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

= e^{2} x (\frac{1}{y + 2} y + 1 \cdot ln (y + 2))

Simplify

e^{2} x (\frac{1}{y + 2} y + 1 \cdot ln (y + 2)) : e^{2} x (\frac{y}{y + 2} + ln (y + 2))

= e^{2} x (\frac{y}{y + 2} + ln (y + 2))

\frac{( e ^{2} x )}{x}

\frac{11}{x ^{4}}

2 e^{- t}

\frac{x}{( x + y ) ^{2}}

\frac{d}{d x} (cos^{3} (x) 3 x (cos (x))^{^{'}})

What is the d/(dy)(ln(y+2)*e^2xy) ?
The d/(dy)(ln(y+2)*e^2xy) is e^2x(y/(y+2)+ln(y+2))
What is the first d/(dy)(ln(y+2)*e^2xy) ?
The first d/(dy)(ln(y+2)*e^2xy) is e^2x(y/(y+2)+ln(y+2))