en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 5x^2*ln(x)

Solution

\frac{d}{d x} (5 x^{2} \cdot ln (x))

Solution

5 (2 x ln (x) + x)

Solution steps

\frac{d}{d x} (5 x^{2} ln (x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{2} ln (x))

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (x^{2}) ln (x) + \frac{d}{d x} (ln (x)) x^{2})

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

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

= 5 (2 x ln (x) + \frac{1}{x} x^{2})

\frac{1}{x} x^{2} = x

= 5 (2 x ln (x) + x)

Popular Examples

(5x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=4

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0, y (1) = 4

integral from 0 to 6 of (x^2-4)

\int_{0}^{6} (x^{2} - 4) d x

y^{^{'}} + 2 x y = x^{2}

derivative of f(x)=(4x^3-2x+1)/(x^2)derivative of

f (x) = \frac{4 x ^{3} - 2 x + 1}{x ^{2}}

limit as x approaches+6 of 3

x \to + 6 lim (3)

Frequently Asked Questions (FAQ)

What is the derivative of 5x^2*ln(x) ?
The derivative of 5x^2*ln(x) is 5(2xln(x)+x)
What is the first derivative of 5x^2*ln(x) ?
The first derivative of 5x^2*ln(x) is 5(2xln(x)+x)