What is the d/(dy)(x^{6y}) ?

The d/(dy)(x^{6y}) is 6x^{6y}ln(x)

What is the first d/(dy)(x^{6y}) ?

The first d/(dy)(x^{6y}) is 6x^{6y}ln(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d y} (x^{6 y})

6 x^{6 y} ln (x)

Solution steps

\frac{d}{d y} (x^{6 y})

Treat

x

as a constant

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{6 y} = e^{6 y l n (x)}

= \frac{d}{d y} (e^{6 y l n (x)})

Apply the chain rule:

e^{6 y l n (x)} \frac{d}{d y} (6 y ln (x))

= e^{6 y l n (x)} \frac{d}{d y} (6 y ln (x))

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

= e^{6 y l n (x)} \cdot 6 ln (x)

e^{6 y l n (x)} = x^{6 y}

= 6 x^{6 y} ln (x)

x \to - 3 lim (\frac{x + 3}{x - 3})

\frac{d}{d x} ((2 x + 1)^{4})

y = 3 - x, y = \frac{x ^{2}}{4}, x = 2, x = 1

3 y^{^{''}} + 2 y = 5 e^{2 x} + 2 x^{3}

\int \frac{3}{2 x ^{2}} d x