en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=6x^4ln(x)

Solution

derivative of

y = 6 x^{4} ln (x)

Solution

6 (4 x^{3} ln (x) + x^{3})

Solution steps

\frac{d}{d x} (6 x^{4} ln (x))

Take the constant out:

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

= 6 \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)

= 6 (\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}

= 6 (4 x^{3} ln (x) + \frac{1}{x} x^{4})

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

= 6 (4 x^{3} ln (x) + x^{3})

Popular Examples

tangent of f(x)=sqrt(5x),\at x=5 tangent of

f (x) = 5 x, at x = 5

integral of tan(5x)sec^2(5x)

\int tan (5 x) sec^{2} (5 x) d x

area x-2,sqrt(x),[0,4]area

x - 2, x, [0, 4]

derivative of [x+(x+sin^2(x))^7]^5 derivative of

[x + (x + sin^{2} (x))^{7}]^{5}

integral of xsqrt(1+2x^2)

\int x 1 + 2 x^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=6x^4ln(x) ?
The derivative of y=6x^4ln(x) is 6(4x^3ln(x)+x^3)
What is the first derivative of y=6x^4ln(x) ?
The first derivative of y=6x^4ln(x) is 6(4x^3ln(x)+x^3)