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Popular >

derivative of 3xln(x)

Solution

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

Solution

3 (ln (x) + 1)

Solution steps

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

Take the constant out:

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

= 3 \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)

= 3 (\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}

= 3 (1 \cdot ln (x) + \frac{1}{x} x)

Simplify

3 (1 \cdot ln (x) + \frac{1}{x} x) : 3 (ln (x) + 1)

= 3 (ln (x) + 1)

Popular Examples

sum from n=1 to infinity of 2-8(0.9)^n

n = 1 \sum \infty 2 - 8 (0.9)^{n}

integral of x^2sqrt(x^3+17)

\int x^{2} x^{3} + 17 d x

derivative of x^{1/2}ln(x)

\frac{d}{d x} (x^{\frac{1}{2}} ln (x))

derivative of (2x^2-5^{-12})

\frac{d}{d x} ((2 x^{2} - 5)^{- 12})

(\partial}{\partial u}(\frac{(u+v))/2)

\frac{\partial}{\partial u} (\frac{( u + v )}{2})

Frequently Asked Questions (FAQ)

What is the derivative of 3xln(x) ?
The derivative of 3xln(x) is 3(ln(x)+1)
What is the first derivative of 3xln(x) ?
The first derivative of 3xln(x) is 3(ln(x)+1)