What is the derivative of f(x)=3sqrt(x)ln(x) ?

The derivative of f(x)=3sqrt(x)ln(x) is 3((ln(x))/(2sqrt(x))+1/(sqrt(x)))

What is the first derivative of f(x)=3sqrt(x)ln(x) ?

The first derivative of f(x)=3sqrt(x)ln(x) is 3((ln(x))/(2sqrt(x))+1/(sqrt(x)))

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derivative of

f (x) = 3 x ln (x)

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

3 (\frac{1}{2 x} ln (x) + \frac{1}{x} x) : 3 (\frac{ln ( x )}{2 x} + \frac{1}{x})

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

\frac{1}{3} x^{3} - 7 x + 5

n = 1 \sum \infty \frac{x ^{n}}{2 ^{n}}

x \to 0 lim (\frac{f ( x )}{g ( x )})

\int \frac{a + b x ^{3}}{4 a x + b x ^{4}} d x

\frac{d}{d z} (\frac{x y}{z})

What is the derivative of f(x)=3sqrt(x)ln(x) ?
The derivative of f(x)=3sqrt(x)ln(x) is 3((ln(x))/(2sqrt(x))+1/(sqrt(x)))
What is the first derivative of f(x)=3sqrt(x)ln(x) ?
The first derivative of f(x)=3sqrt(x)ln(x) is 3((ln(x))/(2sqrt(x))+1/(sqrt(x)))