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Popular >

derivative of 4xln(x)

Solution

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

Solution

4 (ln (x) + 1)

Solution steps

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

Take the constant out:

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

= 4 \frac{d}{d x} (x ln (x))

Apply the Product Rule:

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

f = x, g = ln (x)

= 4 (\frac{d x}{d x} ln (x) + \frac{d}{d x} (ln (x)) x)

\frac{d x}{d x} = 1

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

= 4 (1 \cdot ln (x) + \frac{1}{x} x)

Simplify

4 (1 \cdot ln (x) + \frac{1}{x} x) : 4 (ln (x) + 1)

= 4 (ln (x) + 1)

Popular Examples

derivative of-cos(xln(sec(x)+tan(x)))

\frac{d}{d x} (- cos (x) ln (sec (x) + tan (x)))

area x^3-6x^2+9x+1,x=0.5,x=4 area

x^{3} - 6 x^{2} + 9 x + 1, x = 0.5, x = 4

tangent of f(x)=x^2+x,\at x=-4 tangent of

f (x) = x^{2} + x, at x = - 4

integral from 0 to 1 of e^x

\int_{0}^{1} e^{x} d x

maclaurin e^{x^2}maclaurin

e^{x^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of 4xln(x) ?
The derivative of 4xln(x) is 4(ln(x)+1)
What is the first derivative of 4xln(x) ?
The first derivative of 4xln(x) is 4(ln(x)+1)