What is the derivative of (y(x^2+3x)) ?

The derivative of (y(x^2+3x)) is (dy)/(dx)(x^2+3x)+(2x+3)y

What is the first derivative of (y(x^2+3x)) ?

The first derivative of (y(x^2+3x)) is (dy)/(dx)(x^2+3x)+(2x+3)y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((y) (x^{2} + 3 x))

\frac{d y}{d x} (x^{2} + 3 x) + (2 x + 3) y

Solution steps

\frac{d}{d x} ((y) (x^{2} + 3 x))

Apply the Product Rule:

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

f = y, g = x^{2} + 3 x

= \frac{d y}{d x} (x^{2} + 3 x) + \frac{d}{d x} (x^{2} + 3 x) y

\frac{d}{d x} (x^{2} + 3 x) = 2 x + 3

= \frac{d y}{d x} (x^{2} + 3 x) + (2 x + 3) y

(1 - y + 3)^{2}

y cos (t) + 2 t e^{y} (sin (t) + t^{2} e^{y} + 2) \frac{d y}{d t}

cos (\frac{π ( x + 1 )}{8}) + 148 x - 9062

(0, 8) y (0, - 8)

(3 + 2) 2

What is the derivative of (y(x^2+3x)) ?
The derivative of (y(x^2+3x)) is (dy)/(dx)(x^2+3x)+(2x+3)y
What is the first derivative of (y(x^2+3x)) ?
The first derivative of (y(x^2+3x)) is (dy)/(dx)(x^2+3x)+(2x+3)y