What is the derivative of x^2{z}(x) ?

The derivative of x^2{z}(x) is 2x{z}(x)+derivative of {z}(x)x^2

What is the first derivative of x^2{z}(x) ?

The first derivative of x^2{z}(x) is 2x{z}(x)+derivative of {z}(x)x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x^{2} z (x))

2 x z (x) + \frac{d}{d x} (z (x)) x^{2}

Solution steps

\frac{d}{d x} (x^{2} z (x))

Apply the Product Rule:

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

f = x^{2}, g = z (x)

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

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

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

What is the derivative of x^2{z}(x) ?
The derivative of x^2{z}(x) is 2x{z}(x)+derivative of {z}(x)x^2
What is the first derivative of x^2{z}(x) ?
The first derivative of x^2{z}(x) is 2x{z}(x)+derivative of {z}(x)x^2