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Popular >

derivative of 6xln(x)

Solution

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

Solution

6 (ln (x) + 1)

Solution steps

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

Take the constant out:

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

= 6 \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)

= 6 (\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}

= 6 (1 \cdot ln (x) + \frac{1}{x} x)

Simplify

6 (1 \cdot ln (x) + \frac{1}{x} x) : 6 (ln (x) + 1)

= 6 (ln (x) + 1)

Popular Examples

integral of (e(sqrt(x))/2)/(sqrt(x))

\int \frac{e \frac{x}{2}}{x} d x

derivative of (6(x-3^2)/(3x^2-9x-12))

\frac{d}{d x} (\frac{6 ( x - 3 ) ^{2}}{3 x ^{2} - 9 x - 12})

derivative of 3^{x^2+1}

\frac{d}{d x} (3^{x^{2} + 1})

integral of 3/x+1

\int \frac{3}{x} + 1 d x

tangent of y=4(x-1x)4,\at x=2 tangent of

y = 4 (x - 1 x) 4, at x = 2

Frequently Asked Questions (FAQ)

What is the derivative of 6xln(x) ?
The derivative of 6xln(x) is 6(ln(x)+1)
What is the first derivative of 6xln(x) ?
The first derivative of 6xln(x) is 6(ln(x)+1)