en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 2x^3ln(10x)

Solution

derivative of

2 x^{3} ln (10 x)

Solution

2 (3 x^{2} ln (10 x) + x^{2})

Solution steps

\frac{d}{d x} (2 x^{3} ln (10 x))

Take the constant out:

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

= 2 \frac{d}{d x} (x^{3} ln (10 x))

Apply the Product Rule:

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

f = x^{3}, g = ln (10 x)

= 2 (\frac{d}{d x} (x^{3}) ln (10 x) + \frac{d}{d x} (ln (10 x)) x^{3})

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

\frac{d}{d x} (ln (10 x)) = \frac{1}{x}

= 2 (3 x^{2} ln (10 x) + \frac{1}{x} x^{3})

\frac{1}{x} x^{3} = x^{2}

= 2 (3 x^{2} ln (10 x) + x^{2})

Popular Examples

y^{'''}+y^{''}+24y^'-26y=0

y^{^{'''}} + y^{^{''}} + 24 y^{^{'}} - 26 y = 0

(dy)/(dx)= x/y e^x

\frac{d y}{d x} = \frac{x}{y} e^{x}

(\partial)/(\partial x)(sin(pi(3x-4y)))

\frac{\partial}{\partial x} (sin (π (3 x - 4 y)))

derivative of 5/((6x+5^2))

\frac{d}{d x} (\frac{5}{( 6 x + 5 ) ^{2}})

integral from 0 to 8 of 1/(sqrt(64-t^2))

\int_{0}^{8} \frac{1}{64 - t ^{2}} d t

Frequently Asked Questions (FAQ)

What is the derivative of 2x^3ln(10x) ?
The derivative of 2x^3ln(10x) is 2(3x^2ln(10x)+x^2)
What is the first derivative of 2x^3ln(10x) ?
The first derivative of 2x^3ln(10x) is 2(3x^2ln(10x)+x^2)