en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 3x^5ln(x)

Solution

\frac{d}{d x} (3 x^{5} ln (x))

Solution

3 (5 x^{4} ln (x) + x^{4})

Solution steps

\frac{d}{d x} (3 x^{5} ln (x))

Take the constant out:

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

= 3 \frac{d}{d x} (x^{5} ln (x))

Apply the Product Rule:

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

f = x^{5}, g = ln (x)

= 3 (\frac{d}{d x} (x^{5}) ln (x) + \frac{d}{d x} (ln (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 3 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

\frac{1}{x} x^{5} = x^{4}

= 3 (5 x^{4} ln (x) + x^{4})

Graph

Popular Examples

tangent of f(x)=(4x^2)/(x+2)tangent of

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

derivative of 3+6cos(3t)derivative of

3 + 6 cos (3 t)

derivative of-1/2 t^4+48t^2 derivative of

- \frac{1}{2} t^{4} + 48 t^{2}

tangent of f(x)= 1/x ,\at x=2 tangent of

f (x) = \frac{1}{x}, at x = 2

derivative of (dy/(dx))+4y=2sin(2x)

\frac{d}{d x} (\frac{d y}{d x}) + 4 y = 2 sin (2 x)

Frequently Asked Questions (FAQ)

What is the derivative of 3x^5ln(x) ?
The derivative of 3x^5ln(x) is 3(5x^4ln(x)+x^4)
What is the first derivative of 3x^5ln(x) ?
The first derivative of 3x^5ln(x) is 3(5x^4ln(x)+x^4)