What is the d/(dy)((x)(6x+ln(6y))) ?

The d/(dy)((x)(6x+ln(6y))) is x/y

What is the first d/(dy)((x)(6x+ln(6y))) ?

The first d/(dy)((x)(6x+ln(6y))) is x/y

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\frac{d}{d y} ((x) (6 x + ln (6 y)))

\frac{x}{y}

Solution steps

\frac{d}{d y} ((x) (6 x + ln (6 y)))

Treat

x

as a constant

Take the constant out:

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

= x \frac{d}{d y} (6 x + ln (6 y))

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d y} (6 x) + \frac{d}{d y} (ln (6 y)))

\frac{d}{d y} (6 x) = 0

\frac{d}{d y} (ln (6 y)) = \frac{1}{y}

= x (0 + \frac{1}{y})

Simplify

x (0 + \frac{1}{y}) : \frac{x}{y}

= \frac{x}{y}

e^{4 x} \cdot 4 (x^{2} + 1) - 2 x e^{4 x}

H^{2} + (0.1 t + 1)^{2}

12 (5 (0.675) - 4.5 = 36)

(x y + 2 x y ln^{2} (y) + y ln (y)) d x

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

What is the d/(dy)((x)(6x+ln(6y))) ?
The d/(dy)((x)(6x+ln(6y))) is x/y
What is the first d/(dy)((x)(6x+ln(6y))) ?
The first d/(dy)((x)(6x+ln(6y))) is x/y