What is the derivative of y=x^4ln(x) ?

The derivative of y=x^4ln(x) is 4x^3ln(x)+x^3

What is the first derivative of y=x^4ln(x) ?

The first derivative of y=x^4ln(x) is 4x^3ln(x)+x^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x^{4} ln (x)

4 x^{3} ln (x) + x^{3}

Solution steps

\frac{d}{d x} (x^{4} ln (x))

Apply the Product Rule:

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

f = x^{4}, g = ln (x)

= \frac{d}{d x} (x^{4}) ln (x) + \frac{d}{d x} (ln (x)) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 4 x^{3} ln (x) + \frac{1}{x} x^{4}

\frac{1}{x} x^{4} = x^{3}

= 4 x^{3} ln (x) + x^{3}

x \frac{d y}{d x} - 4 y = x^{6} x^{x}

\int 50 + 3.5 x e^{- 0.01 x^{2}} d x

y^{^{'}} = x e^{x^{2} - y}

y^{^{'}} = \frac{( 3 x ^{6} e ^{\frac{y}{x}} + x ^{4} y ^{2} )}{x ^{5} y}

What is the derivative of y=x^4ln(x) ?
The derivative of y=x^4ln(x) is 4x^3ln(x)+x^3
What is the first derivative of y=x^4ln(x) ?
The first derivative of y=x^4ln(x) is 4x^3ln(x)+x^3