What is the derivative of-3xyln(xy) ?

The derivative of-3xyln(xy) is -3(ln(xy)y+xln(xy)(dy)/(dx)+y+x(dy)/(dx))

What is the first derivative of-3xyln(xy) ?

The first derivative of-3xyln(xy) is -3(ln(xy)y+xln(xy)(dy)/(dx)+y+x(dy)/(dx))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (- 3 x y ln (x y))

- 3 (ln (x y) y + x ln (x y) \frac{d y}{d x} + y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (- 3 x y ln (x y))

Take the constant out:

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

= - 3 \frac{d}{d x} (x y ln (x y))

Apply the Product Rule:

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

f = x, g = y ln (x y)

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

\frac{d x}{d x} = 1

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

= - 3 (1 \cdot y ln (x y) + (ln (x y) \frac{d y}{d x} + \frac{y + x \frac{d y}{d x}}{x}) x)

Simplify

- 3 (1 \cdot y ln (x y) + (ln (x y) \frac{d y}{d x} + \frac{y + x \frac{d y}{d x}}{x}) x) : - 3 (ln (x y) y + x ln (x y) \frac{d y}{d x} + y + x \frac{d y}{d x})

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

\int_{0}^{1} x^{10} + 1 0^{x} d x

\int 6 x e^{7 x} d x

\frac{\partial}{\partial x} (2 x - 3 y + 4 x y)

\int \frac{2}{1 + 3 x} d x

r \frac{d r}{d θ} = sin^{2} (θ)

What is the derivative of-3xyln(xy) ?
The derivative of-3xyln(xy) is -3(ln(xy)y+xln(xy)(dy)/(dx)+y+x(dy)/(dx))
What is the first derivative of-3xyln(xy) ?
The first derivative of-3xyln(xy) is -3(ln(xy)y+xln(xy)(dy)/(dx)+y+x(dy)/(dx))