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Popular >

derivative of 2x^4ln(x)

Solution

derivative of

2 x^{4} ln (x)

Solution

2 (4 x^{3} ln (x) + x^{3})

Solution steps

\frac{d}{d x} (2 x^{4} ln (x))

Take the constant out:

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

= 2 \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)

= 2 (\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}

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

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

= 2 (4 x^{3} ln (x) + x^{3})

Popular Examples

integral from 0 to 1 of pi(x^2-x)

\int_{0}^{1} π (x^{2} - x) d x

integral from 0 to 1 of ((1+e^x))/(e^x)

\int_{0}^{1} \frac{( 1 + e ^{x} )}{e ^{x}} d x

integral of (x^2)/(sqrt(9-4x^2))

\int \frac{x ^{2}}{9 - 4 x ^{2}} d x

derivative of a^x*x^a

\frac{d}{d x} (a^{x} \cdot x^{a})

x+2xy^2+e^{x^2}y(dy)/(dx)=0

x + 2 x y^{2} + e^{x^{2}} y \frac{d y}{d x} = 0

Frequently Asked Questions (FAQ)

What is the derivative of 2x^4ln(x) ?
The derivative of 2x^4ln(x) is 2(4x^3ln(x)+x^3)
What is the first derivative of 2x^4ln(x) ?
The first derivative of 2x^4ln(x) is 2(4x^3ln(x)+x^3)